IM 7.6.8 Lesson: Reasoning about Solving Equations (Part 2)
Select [b]all [/b]the expressions equivalent to [math]2\left(x+3\right)[/math].
Explain why either of these equations could represent this hanger:
[math]14=2\left(x+3\right)[/math] or [math]14=2x+6[/math][br][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALYAAAEqCAYAAAC4I6qIAAAgAElEQVR4Ae2dC9xNVfrHzR+VS5OKUClJaBTpQgih0gUV3U03MiZdh9JEISQqTUbSxSikMjLIqDSKShJJMSVCokjpfplr8/w/3+fz2W/H2+uc/Zyzj/3a51mfz/68+5z97LXP/u3vXu+z1nrWWmXEkyuQQAXKJPCe/JZcAXGwHYJEKuBgJ/Kx+k052M5AIhVwsPP0WP/973/Ll19+KR999JFs2LBBvvnmG/nxxx/zdDXPtrgCDnZxRSL6/MMPP8iCBQvkpptukj59+sjrr78u//nPf+R///tfRFfwbNIp4GCnUyeHY19//bX88Y9/lF/+8pey2267ycSJE+Vf//qXg52DppZTHWyLWgZbwB49erTsueeeUr58eQfboF0Upg52FCqWkIeDXYIoO/ErBztPYjvYeRI2ZLYOdkihrGYOtlWxaO0d7Gj1LMrNwS6SIpYdBztPsjvYeRI2ZLYOdkihrGYOtlWxaO0d7Gj1LMrNwS6SIpYdBztPsjvYeRI2ZLYOdkihrGYOtlWxaO0d7Gj1LMrNwS6SIpYdBztPsjvYeRI2ZLYOdkihrGYOtlWxaO0d7Gj1LMrNwS6SIpYdBztPsjvYeRI2ZLYOdkihrGYOtlWxaO0d7Gj1LMrNwS6SIpYdBztPsjvYeRI2ZLYOdkihrGYOtlWxaO0d7Gj1LMrNwS6SIpYdBztPsjvYeRI2ZLYOdkihrGYOtlWxaO0d7Gj1LMrNwS6SIpYdBztPsjvYeRI2ZLYOdkihrGYOtlWxaO0d7Gj1LMrNwS6SIpYdBztPsjvYeRI2ZLZ5BZsJGP/xj3/orKPMPFpIG7Osjhw5UipWrCjlypWTcePGyaeffipffPFFQenALLNM0Pnf//43JJLRmOUNbKBmKt2XXnpJ7r777oLbbr/9djn77LN1Qsr/+7//kwsvvFDuvPPOgtNhzJgx8uqrryrc0SAbLpe8gv3dd99J//79pUKFCgW37bHHHlpSA/UvfvELnZiS7wpNi3333Vd4yb/66qtwREZklXewb7zxRilTpoyULVtWdt99d519lKl1fUuuBswwywvMC125cmUZPHiwumARMRsqm50CNjeIr3nmmWfqJOj9+vWTpG68yOnuLdPxdOfuCse4v759+0qXLl20MEs02Pw75i2ePn26LllBhdK35GqACzpr1ix1xRIP9l577aU3S4XSU3IVoNGAFpBnnnlG6xUOdnKfdUHdmYNdUI+7cG7WwS6cZ11Qd+pgF9TjLpybdbAL51kX1J062AX1uAvnZh3swnnWBXWnAdhz5szR5r5KlSrJoEGDktnzSAeNt2MXBt+AzdLaf/3rX7cD+/PPP9+pAuyULnUHe6c+0512saB0ZiltQlMJUSUsd+PGjfLQQw9pzyOBX1dddZW88847eow49e+//16X36YjhzzykRzsfKhaIHn++OOP8s9//lMojZcsWSL333+//Pa3v9U4kWOOOUZjRYhFP/TQQ6Vjx45yxRVXaNguoczEpnMueeQjOdj5UDXBeQauBqXzli1b5JFHHpHzzz9fmjZtKocffrgcfPDBUqtWLTnkkEOkSZMmuh122GH63UEHHST169eXY489Vs466ywhVpvSnVKcUj/K0tvBTjCEUd9aUEID4osvviinnHKKEG+9zz77KNBE9AH6smXLdJQQ8GNLLDauyNSpU6V79+5Sr149PYdzjz76aPnzn/+sbgpwRzXSxsGO+uknND+gxo8GUMJSKZFr164tbdu2lbFjx8q6devUd8a9INCNCiSQsrHPdxwjD4bNPfHEExrGDOQ1a9aUyy+/XBYvXqwvQhTuiYOdUBCjvC3gpMK3aNEi9ZMPOOAAad26tQwfPlzWr1+vwFrcCMAFdNwQxoJ26NBBcFM6d+4sNBNSyvMy5JIc7FzUK5BzKWXnz58v7dq1kxo1ash5552nrggx9UBqgTpVMs4D8JUrV8qVV16pJXezZs20NOea2ebLNRzsVKV9fzsFgpJ16dKlcvLJJ8v+++8vvXr1khUrVqhLkQt4wYUCuHFlBg4cKHXq1JFGjRrJvHnzhAEL2SYHO1vlCuA8SlP84W7dumllj6F9uA9RAF1cPl4iKplXX321VK1aVU488UR5++23s/6P4GAXV9g/FylAZ8uwYcO0koiLsGHDBnUdigwi3OFlAe5PPvlEK5XA/Zvf/EY+++yzrPxtBzvCh5OUrICMytsrr7wizZs3l4YNG6pPTXNcvhPXff/996Vx48Zy1FFHaVNgNi6Jg53vJ7UL5k8rCL2Jt912m06TwdwwuAmUqPlOvFRUHOnFpDnxoosukrVr15ov62CbJUv+CZTMtFRQWtM1Thc4sGfyrTnOhm3xl4DPbGHyCUptZtKiaZGBwdb/Fg528jk13yEl5oQJExSqG264QbZu3RoqjwBqmgEBMXgR+MtnOmj4C9zpUmD/4IMP6nw0Q4YMMYe9OtjpFC7QY99++61ccMEFGtfx2GOP6RwwYaSgRKYTh2g+muuCkhuYV61apS0eDzzwQKjpzoD7hRdekCOOOEI6depkdkcc7DBPrIBsgJPIO3oC27RpI2+99VboVgnOpTmQdmgCo+hBpMeS3slzzjlHWrRoIS+//HLolhUqkeSDr815luRgW9QqAFvarl977TWdc48eRlokApcizO1TOjNihlYNAqXeffddndYOf/2pp55SqMPmx7TTAwYM0MjA++67L8zli2wc7CIpfAcF8IMJUKpSpYq6DmEhDNSj4gfMhLHSTU48yfHHHy+PPvqoviSU6mETpT0BVnXr1hV8fUtysC1qJdwWiKk43nvvvVK9enVt7rPeMuCSB02E5IGPDNzZDA2jEkpIK3l07drV9FMcbJNcyTYOwGaifuJC7rnnHvMNU2HEt3722WfVnWHCe0pw/hNYE2DPnTtXByZQgbQkB9uiVsJtA7BHjRqlkXZ33XWX6Y4prQF49erVGjRFiX3qqacKQVTZgj179mwdhUOciiU52Ba1CsAWAGk/ZlQMc11bEueuWbNGfv3rX2u8NnEm+NdU/CjFrQkfe/z48dKgQQONA7ecv0Owefty2fiXxNAgnP5glPrMmTP1zc0lX86lZGHzFL0CtIo899xz2pV+6aWXaisGmqdLPAueN816jK5hrCMtIB988IH07NlTS22aAbGxJPi54447tLmP5T4saYdgc4O5bLy9NNdwo4DN0hx/+ctftF0zl3w5F4EcbMtjDm8LxMRGMw/MaaedJh9++GHGdmyeB5GAVBIZrDt58mStQPI9JS7fUajhM1ueGyGzRPgdeOCBumhA+LtIM9Bg4sSJMmnSpJw2buqMM85QsFmTBMhp9sklX5qiWIUqm4gvizCFagt4lJQtW7bUgbYM1QLIdIm2aybIoUNn6NChWqAFpTMBTMR8MIgXu7BgY8eUDq1atdJ4FSqglrTDEpuJTpiNHl+L0cTZbrz5THPFUh20jWabD+eRF3/598bQf0/5UYDmOiL7mEqBtSoz+ceU8vwn5b80W6rrQrs23wF1AHumXw3UnDdt2jSpVq2atoeHjVcJ8t4h2LgPdGX26NFDevfurf3/xABYN86loZ4tl3wYkkTNeL/99tO3f/PmzcE9+N+IFQBCIvqCiW4YmZ6upOUYMAdbqm3qsdTv0/1koGbAAfUzCkT+y/NyWNIOwWYJOwZv4udQO+UtjnOj1CAohsGkDNX/+OOPLffptgYFKFnR95JLLtGChLlCCIxKLYkN2ZlMgR/Onn/+eY05wSVinpKwL0VwsbRgM4Bz27ZtRZU1Mo9r440lEIaOA/w1Bzt4hNH/5RnjWtDrRzAUbdE041GS5zvx8jCogehCPAba1GmEsKa0YDPTD2DvjDc10w9HVMAm8NzBzqRW7seBmxYR5tujVYI2bQAD+HylAGravfnPTKsMblA213Sw8/WUEpAvhQkRescdd5xW/B9++GFtMQFAwI8y4f7wX3nGjBn6X5mZpnCBsr2Wgx3l00lYXkBFaRm0ReMaTJkyRUeOZ1OKliQPLwjXoR2cjiFGwzPlGaNm8OuzTQ52tsoV0Hm4IHS+ADaDCEaPHq1TMdC+TUmbbekdlNI05fHC0GaNT89UxEQDcjzb5GBnq1wBnUeJCtwAzQAC4Lv++uu1A4UWs2wAJE9aPwiYGjx4sL4wvDi33HKLtsRlk2fqI3GwU9Xw/R0qAGjATUsJJSs+MD2NI0aM0PGMHKM3GD8ZN4W2aM4JNr7jGC8CrR5UTJligRYX2suZTpj5smnt4txs/wsEN+BgB0r431AK4H4sX75cW6YIS2XGJkpxWk2oaOJW0CWf2vfBPv4y7gUhrPjPjH+ks23vvfdWuOmjIG9K8iiSgx2FigWUB+BR+gIq8SE0yQUrGVDpo+Rl4C69hpTmbDfffLPO/0cIKzaseEBgVPv27TVgitKe0py8cy2pg0fhYAdK+F+TAgCIy0BrBqNlbr31Vl1+g1YNhnLR30C8UcWKFbVUB2TGQeJ6EAxHWCvxPjQpRgVz6g042Klq+L5JAYDEhwZwSlxAZYT7rFmztMQuX768ENXJejPMT7Jw4UL1rXE5KPU5Nx9QcxMOtulRunE6BXAlgBxwn376aV0OjxKb0py5SjgWpbuR7rc42OnU8WNmBYJSnPn2KLEJfaY5D5dlZyYHe2eqXQDXcrCND9mDoIyCxWTuYBuFd7CNgsVk7mAbhXewjYLFZO5gG4V3sI2CxWTuYBuFd7CNgsVk7mAbhXewjYLFZO5gG4V3sI2CxWTuYBuFd7CNgmVpDpj0Dgbhpta/9C7yrAiQKleunM4pw4q7rNdozau4veWWvIPGolYB2AI1cRx0i2c73QaRf0xpBth0qTN4gDiSbPPjPH6PJTnYFrUKwBaAGETbr18/jcIj/NS6Eb1H6Cpd6kT4nXDCCXLNNdeY80m9Lt3yluRgW9RKuC1uCBMTnXvuuTqdHFPKMcWYdWPwAVPRMaUdG9Pk8V02+XAu8SYMG7MkB9uiVsJtA7BZVIl4auZIZFWDbDYmumFlBDb22az5MPF8nz59pE6dOjo4wSK/g21RK+G2gM14RMCuV6+esJoAcdZxbYyhXLx4sU7JwItmSQ62Ra2E26aCzSoChJ7yXVwbrSvM28eQMgc74fDl8/aKg82QrzgTrTNvvvmmrunuYMf5JHbxazvYMTxA76DJv+gOdv41/tkVHOyfSRL5Fw525JJmztDBzqxRrhYOdq4KZnG+g52FaMZTogCbPIjxoOLHM2NjP5vR6V55ND5ANy9ZgVzBDqCmW554EdrE6clkH8CB25IcbItabrtDBXIFm6nK3njjDZ3SjGVemHL4yCOP1NmfmKmVRUyJ/gubHOywSrldWgVyBZv1N1nXs0OHDrpCHKvpsqwe68kE814zv0jYktvBTvu4/GBYBXIFmyXsCFddtWqVhqjSFY9bwspzRPsxXfCCBQvU5w7zmxzsMCq5TUYFcgWbSmPxaczIE8CHDRumC6Iyvzb+dpjkYIdRyW0yKpAr2CVdALeDUpsFbJksfv78+V5ipwrFW+7L4aUqEv1+FGADMhO940szEeWmTZt0ZV2mEe7atau2kLiPnfLsHOwUMfK0GwXYuCNMJUwcNaX0SSedJHXr1pXLLrtM15vBveA6YZK7ImFUcpuMCkQBNqUxMdTXXXed9OrVS2O7O3XqpCsaTJgwQUty4A+THOwwKrlNRgWiAJs8cEVwQ2gNYWVd1m9kXXbatVnJAJ87THKww6jkNhkViAJsLkI+wUYJDqAsyERzH8uF0xsZJjnYYVRym4wKRAE2eRRPNAFu3rxZeyEZduZgpyjklccUMfK0myvYQYcMILMF7drMC0IzH72PvXv31paRMLfgJXYYldwmowK5gs1ajRMnTpS//e1vup7jypUrtSJJpwzd7E2aNJG5c+d6B03qk/ASO1WN/OznCjYrg7Vt21ZX7KUL/eKLL5YzzzxTWrZsKZ07d5Y//elPWrH0duyU5+dgp4iRp91cwSZWhEAoSuixY8fqnCLAzKBgWkdoDeEaYZO7ImGVcru0CuQKNj41BRDNfcRi0/vI8tMAjc9tgZof6mCnfVx+MKwCuYId9jph7RzssEq5XVoFHOy08uTnoPvY+dE1NVcHO1WNnbTvYOdfaAc7/xr/7AoO9s8kifwLBztySTNn6GBn1ihXCwc7VwWzON/BzkI04ynFwfbZVo0CZmPuYGejmu2cVLAZHDB16lQNPyUENY6NwCm66Y855hifRtj2KN06VYEAbLrDWWrjlFNOkcsvvzy2jVE3dMVXr17dwU59UL5vUwCwWUWgW7duUqNGDV0zpmbNmmLZOI+NF6NChQq6HF6wlo0lH2zJB6hZu6Zhw4amm/EVDUxyJd+Y3r7Vq1fruEXiPqzbwoUL5ZVXXtE1Z8qWLaurhl1xxRUa1WfNK9V+6dKlJvEdbJNcyTcm8o64jiC2mjgPy0bsNaV+Ses8WvIpydaivoNtUcttMyqAO0MwFC0qrPPIUnas0UhA1M5MDvbOVLsAruVgGx+yN/cZBYvJ3ME2Cu9gGwWLydzBNgrvYBsFi8ncwTYK72AbBYvJ3ME2Cu9gGwWLydzBNgrvYBsFi8ncwTYK72AbBYvJPHFgc0PAR89T2BHJwbxu9FTR05UuOdjp1Ck9xxIFNoACNAu6P/7447J+/fpQC+gQl8B8E6NGjZI5c+akfToOdlp5Ss3BRIDNTVA6b926VSZNmiStWrXSSKzp06frnBAc31HiZVi7dq3OFET0FnMpp0sOdjp1Ss+xRIANnFu2bJHhw4dLu3btpFmzZgr2k08+qW7JjsAmloAJVYghaNy4sS66Q9xvuuRgp1On9BxLBNiU1kxl1aJFC7nvvvtkxIgRUqdOHZ3iChB3BDZuC6MzmjdvLuPGjZMGDRrovMnpHo+DnU6d0nMsEWBT8rLaKlPEEr3FUgxM7h0seVYcbD7zMuCLM1lh3759Zd26dbqaFBOCp0sOdjp1Ss+xRICNnNxIAPDkyZPTgs2LsG3bNhk4cKC0bt1aVqxYISxTzMvgrkjpgTOXX5IYsFNFSAc2N8xkhVOmTNGVpJhylgkL8bUd7FQVd+39ggKbm6Vpj4nAGSDav39/rXTilrBsg4O9a8Oc+usLCmxaT5g7uUePHtKxY0d566231Nfm+6DEZkQyorCVlNzHLkmV0vddQYGNbz1y5EipXbu2tqIsW7ZM3nvvPd2oSNaqVUu6dOmin3kBKMmLA+5glz6IS/pFBQU2oNLGXalSJalSpYoOza9ataqwMTS/XLlyOlSfz9dee61WKCnNU5ODnapG6d0vKLCBlPZqOmSGDBkiQ4cOLdoGDBigoDPbD9/Pnj1bu+e9xC698Kb7ZYkFm6mxpk2btl3PIzdL5bGkIfWfffaZduqwcivHKd2Ll9YI6SV2OpxKz7FEgk1THr2ILCsMyKmlLrCWtNEqUr9+fa1Ycjz1nNTH5WCnqlF69xMJNjP39OvXT5YsWaIlbxj5KaVvvPFGGT9+fFpzBzutPKXmYCLBJqaaEhgId1TyFn8ClNKcQ+dNuuRgp1On9BxLJNjBTYWFmscRnAPg6ZKDnU6d0nMseJ4+E1TIZ+JghxQqZjMH2/gAHGyjYDGZO9hG4R1so2AxmTvYRuEdbKNgMZk72EbhHWyjYDGZO9hG4R1so2AxmTvYRuEdbKNgMZk72EbhHWyjYDGZO9hG4R1so2AxmTvYRuEdbKNgMZk72EbhHWyjYDGZO9hG4R1so2AxmTvYRuEdbKNgMZk72EbhHWyjYDGZO9hG4R1so2AxmTvYRuEdbKNgMZk72EbhHWyjYDGZO9hG4R1so2AxmTvYRuEdbKNgMZk72EbhHWyjYDGZO9hG4R1so2AxmTvYRuEdbKNgMZk72EbhHWyjYDGZO9hG4R1so2AxmTvYRuEdbKNgMZk72EbhHWyjYDGZO9hG4R1so2AxmTvYRuEdbKNgMZk72EbhHWyjYDGZO9hG4R1so2AxmTvYRuEdbKNgMZk72EbhHWyjYDGZO9hG4R1so2AxmTvYRuEdbKNgMZkDNiu/zZkzR8qXL69rew4aNEg+//zznfqLyuzoamXKlNF1z7dt21bi8nQ7Oi9f3zvY+VI2t3yDEppV4liD6IcffpAtW7bIgw8+WLQw7dVXX62rLnMMG2xZrTnT8iy5/DIHOxf1CvxcoKbA+eqrr2Tx4sUyYsQIXTq8VatWUq9ePSlbtqyW2gcccICuzNypUye55ZZbZN68ecL6npybL7gd7AKH03r7QQlN6Yt7Qcncvn17XYS2Vq1aUrNmTd2A+cgjj5RGjRrJwQcfLDVq1NDvDzzwQDnkkEOkZcuWctddd8knn3yipTzuS5TJwY5SzQLICwBxT6dPny5t2rSRvfbaS/bff39p0qSJLkL7+OOPy1tvvSVffPGFluSU5l9++aWsWrVKZs6cKddff70cf/zxwkuw9957yxFHHCEPPfSQbNq0Sd2TqCR0sKNSMuH54DKw2OyyZcvkqquuEpYWP/zww+WCCy6QRx55RH1oYP7222+1BMaXxtVgC3xvjgH5Bx98oC9Gjx495KijjhJK8YsuukhefPFF+eabbyJxTxzshAMZxe0BNYDOnz9fzj33XKlevbp06NBB7r//foUU4LHBTQmTgvwopSnhyRO427VrJ1OnTtUXA5tckoOdi3oFci4l7nPPPacVQAC87LLLZNGiRUWrMFsh5AXgHFpHvvvuO3n33Xfl97//vRx00EHSuHFjXX6ca4Z9UUp6DA52Sar4d6pAUFFcsmSJtGjRQit/+Mhr167VJcJzAS+QOCi9P/roI7njjjvk0EMP1crl3Llz1fUJ7Kx/HWyrYgVkT1vzxo0b5eyzz9aK3oUXXiibN2/WSl4UUKdKSaUUH7xfv35SrVo1rWAuXbo061LbwU5V1/e3U4DWj9tuu02b6/Cp169fn1Mpul3mxT7wogA3JTeuzn777Sfdu3fX5kBeMGtysK2KFYg9LsKCBQvkmGOO0aY8WiyoJOY74XevW7dO/fmGDRvKk08+qW6P9boOtlWxArAHajpf+vfvr+3UQ4cO1c/ZlJxWubg2FcoJEyZI7dq1tTlxzZo11mzEwTZLlvwTKDX//ve/a0ndtGlTefXVV9VNCONXYwOcxW2D70s6VlxRrv/+++8r1Lgks2fP1usXt0v32cFOp06BHsPloDeQbvGbbrpJ4zrCSAG8lOq0eRfvIg++51imkh/4ae579NFHpWLFihpfQseOJTnYFrUKxBZXoGvXroKPO2XKlNA+LkDSktGzZ08tZQEY2CmBX3/9denVq5f2UtK7mCmRFx1CxJoEFddM56Qed7BT1fB9BZGwU0pregJXrlypYIaRBhg//vhjwX0566yzNFYEqIkTOf300+Wkk04S2sQptcMk2svpssfXpvJqSQ62Ra0CsMWFWLhwoey5555CuzWlN8CGSZTOuBBE7RHZR2/lO++8I1deeaUGTD3//PN6PGx+uB+EudIjOWbMmDA/ocjGwS6SwndQgNJ08uTJUqVKFbnuuut+VgnMpBIvBhU/IviuuOIKGTBggBx77LEa2WcNcOKlGjt2rBx22GHSt2/fTJfe7riDvZ0chf2BEpc461GjRmmg07Bhw8yCUBrTgzh8+HDZd999NQoQOIn8y1RpLH4xKrFPPfWU+tm4NpbkYFvUSrhtAPbdd9+tMdb33HOP+Y4Bm5KZeO3KlSurj4w7kk3nDucQM0KJz+gbS3KwLWol3Bawv//+ey2xGQkzcuRI8x3jirzxxhvqUzOYoG3btqYKY+oF8ddnzZqlMdteYqcq4/tmBSgl6fXbZ5995IYbbjCdTwsIrSgETdEKQonP+Mc//OEPGuJqykxE3aKHH35Yx0/SVGhJXmJb1CoAWyqPtF7QKnLJJZeE6nGkpMcFIUgKAIkvoUVkw4YN0rt3b2ndurVGCYZtDQlkxlcnlJUxk/y1JAfbolYB2FLB+/DDDzVGhI4RhnFlqvRxnMohLSD169eXZ555Rv1sXpJJkybpEDKCmfjMSxA2EelHZw9t6rgkluRgW9QqAFvAo/J34okn6mgW4jTwddMlgJ0xY4accMIJQsWTAbz42uRFKc7Qr4svvtgMNlM6kCdNh4yysSQH26JWgdhSgaS5jsofLgCgpku4GMBPUyFbagmP3813HA9gT5dXcIw8n3jiCW0ypD2daRosycG2qFUgtkD48ssvS4MGDeTUU0+VFStWpHUhKJmBGXCLwwugfMfxsD42toDMDFJM7/DYY4/py2GR38G2qFUgtoAY+Ld0sjApDqWuxT/ORSpeLPx0pndg7pLly5ebr+1g5/IEEnouAAMXfnOdOnW0VYOAJNyKfCdKdXx8OmQY2HvvvffqXCTW6zrYVsUKxB64KbVpvqOzhkAmmt9S/eeopeCa+Pd0DNGO3rFjR1m9enXoaMDU3+Ngp6rh+9spQGcNvjbt0ARFEUOSqSK5XQaGD8F/CZoHmTIN/57KIy8Sx6zJwbYqVkD2QAXcDDZgjj3cknHjxmnFDj88qoT7wRhLAp6OO+44bY2ht5Kw1Wyg5nc52FE9nQTnQ+cLEXr0ANIBQ1Ng0HGTLXjIxbm8PEDNC0OwEzNN3XzzzTrxZS4vj4OdYCCjujUqjcwxQslNiUrg/+WXX67TnFGiZ+N3AzUV1Pfee0/69OmjLSDMqY27g2/PNXN5aRzsqJ5+wvOh9KTkJgaEwCb8YNwTutEZWEClD1CxA3Tci9SN7zhGLyW2zChFL+XRRx+tXeb8ZdbWrVu35gw1j8LBTjiQUd0epSegAiVTM1x77bXqc9N6wQgXWk2I58BFYbUCKpmMgGH7+uuvtcSnJGYSHka+M/kkbeTEgZx33nla+tNWDvy5lNTB/TrYgRL+N5QClLy4H/jFzz77rEYAMmElvjcuCn4yYavMoc14RTa6xBmU27x5c/XTee5W5CUAAAZISURBVBGaNWum3zFtMKV0MLYyCqi5EQc71ON0o+IKUHoHvjcjyPGNmcidke24FcSZVKhQQecFYdIbBvcSWMUE77fffrv2LDIaHvclKphTf6ODnaqG74dWIHBNgBsXgt5CXA1WPHjhhRdkyJAhsttuuynY3bp1k6efflrnHMFVwU3BpcHfzqbiGeZHOthhVHKbUAoEpTig42+XK1euaCanoFKITT5K6OI/0MEuroh/zkkBoKUCWNICpjsD6ODHpwWbmXsIH+RfBj82zo1/XdSoaWaiDZUZhzyVPgWAF/eC6DxW5mWk+uDBg7WpcGf+2rRgM1UVNV9mBmLGzTg3oKb3i/UCHeydiYjtWqUebPyjqlWrak8TzTQ06cS50Tz0q1/9Sts+qX3TwO+p9ClQ6sE++eSTdZbL0047TUrLxuDSzp07a48VXbyeSp8CpR5smm7wY0vbhs9P1BfNTJ5KnwKlHmwqjKVxA2gqJwjoqfQpUOrBLn2S+S/aFRRwsHeFp+S/0ayAg22WzE/YWQoAZ7YbPYvpOmiyzZfzLGmH7diWTNw2OQoAEHUY6jLZ1rGI/iM2hCbjSpUqya233qoRfNnmx2+xNhY42MlhMpI7AT5CSRn+xcTv2WwEQDGhJT2PRPi1b99eByRkk1dwDtMwWJKDbVEr4baU1kyxQOw0gwAIX2Bho2w2wlarV6+uPcXkw3jJbPJhDCSDGRg2ZkkOtkWthNsCNqNdGNECmIxFHD9+fFYb81o/8MADOosUa0by2ZoX5w0cOFBH6PBiWJKDbVEr4baATaw0YFNC4ifjL8e1EeO9aNEiXV6PIWSW5GBb1Eq4bSrYTFhDhB4Vybg2RtewICrTCDvYCYcvn7dXHGwiO+NMtIS8+eabOlbSwY7zSezi13awd/EH6D+/ZAUc7JJ18W93cQUc7F38AfrPL1kBB7tkXfzbXVyBqMAmXoSWFGJGghYV8rYmrzxaFXP7EhWIAmxApi2cyXA2btwomzZt0gHhzPRkhdvBLvEx+ZdWBXIF+9NPP9W1z5nSjEWZWrZsqeNkGVo4dOhQWbVqlZbgYX+Xgx1WKbdLq0CuYNNLyNoxxJoMGjRIZxUYPXq0zuPHpPHMCMWElWFLbgc77ePyg2EVyBVsoH3ppZdkzZo1Oi6VuBPcElySSy+9VOrWrSvz5s1T3zvMb3Kww6jkNhkVyBVs/GvCXvkblMr8pWs8WBOdkFhswiQHO4xKbpNRgVzB5vxgCy7GZ+by6969u86nzWJNABsmOdhhVHKbjArkCjYXIA+i8nA/mFl15cqVMmbMGGnUqJH07NlTj1Gih0kOdhiV3CajAlGADbT42UxDF0z2TggsKx6sW7cutH/Nj3WwMz4yNwijQBRg0znz9ttvy5133qmTUfbu3Vu6dOkip59+ug43YwYvbMIkBzuMSm6TUYEowCYPZsalhYT5FVl46bXXXpNrrrlGVwZjgVKvPGZ8FG4QpQJRgM3vCaZgoMQFYnodWTqatdFp9mNcZZjkJXYYldwmowJRgV38QsSMMBcky+fhd9O+HSY52GFUcpuMCuQKNs16wFg8UWrPnDlTR6r/7ne/c7CLC+Sf86tArmCzPAeLkk6bNk1or2a8IgstsZx0mzZtdAk8vmdwcJjkJXYYldwmowK5gk2vYtu2bXU5PJa+IxCKVXxZ+/H888+XGTNmFK3nmPHHeHNfGIncJowCuYLNktSsjc6SLtOnT5fJkyfrSPfly5fLhg0bijpnuE6Y5CV2GJXcJqMCuYJNJRE3g1YPKohM0E8vJM1/QBq2/Tr4oQ52oIT/zUmBXMHmfDYAZqMXMtjne2tysK2KuX2JCuQKdomZ5vClg52DeH7qTwo42D9p4XsJUsDBTtDD9Fv5SQEH+yctfC9BCjjYCXqYfis/KVAS2HwX10blcdmyZT7b6k+PyPeyUSAVbAYH0DVOp0tcG9M5LFiwQJc999lWs3mifo4qEIB9zjnn6FIdTZs21SW+WeY7ju2MM87QGJNq1ar5/NjOaPYKBGB37dpVKlasKHvssYfsueeesW2VK1fWVcd23313Bzv7x+pnJkkBX6ojSU/T76VIAQe7SArfSZICDnaSnqbfS5ECDnaRFL6TJAUc7CQ9Tb+XIgUc7CIpfCdJCvw/8w978AMVALUAAAAASUVORK5CYII=[/img]
Find the weight of one circle. Be prepared to explain your reasoning.
Here is a balanced hanger. Each piece is labeled with its weight.
[img]data:image/png;base64,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[/img][br]Assign one of these equations to the hanger:
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.
Here is a balanced hanger. Each piece is labeled with its weight.
[img]data:image/png;base64,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[/img][br]Assign one of these equations to the hanger:
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.
Here is a balanced hanger. Each piece is labeled with its weight.
[img]data:image/png;base64,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[/img][br]Assign one of these equations to the hanger:
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.
Here is a balanced hanger. Each piece is labeled with its weight.
[img]data:image/png;base64,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[/img][br]Assign one of these equations to the hanger:
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.
IM 7.6.8 Practice: Reasoning about Solving Equations (Part 2)
Here is a hanger:
[img]data:image/png;base64,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[/img][br]Write an equation to represent the hanger.
Solve the equation by reasoning about the equation or the hanger. Explain your reasoning.
[size=150]Explain how each part of the equation [math]9=3\left(x+2\right)[/math] is represented in the hanger.[/size][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKMAAAF7CAYAAAC+djt2AAAgAElEQVR4Ae3debh9VVkH8P6yfIwZESRkTJkEZZCAUkFQZEwZRCrFEFRkiEECZAzJEJUfIqYyCDIJyiAIOIQEqSkJYmSZ4VCUzdk81+75rNuC8zvuYa1z9j733t9Z63n2c+7de+3pfb/7nda73vUj1cDt29/+dvV3f/d3A9+lXH4oCvzZn/1ZZZtF+5FZ3KTco1AghQIFjA1U+pd/+ZfqG9/4RnXXXXdV999/f/X3f//31X//93839C67+6BAAWMDFYHvQx/6ULX77rtXBx54YPWXf/mX1X/913819C67+6BAAWMDFf/mb/6muuCCC6p11lmn2mabbaonnnii+s///M+G3mV3HxQoYGygYgFjA2EG3F3A2EDcAsYGwgy4u4CxgbgFjA2EGXB3AWMDcQsYGwgz4O4CxgbiFjA2EGbA3QWMDcQtYGwgzIC7CxgbiFvA2ECYAXcXMDYQt4CxgTAD7i5gbCBuAWMDYQbcXcDYQNwCxgbCDLi7gLGBuAWMDYQZcHcBYwNxCxgbCDPg7gLGBuIWMDYQZsDdBYwNxC1gbCDMgLsLGBuIW8DYQJgBdxcwNhC3gLGBMAPuLmBsIG4BYwNhBtxdwNhA3ALGBsIMuLuAsYG4BYwNhBlwdwFjA3ELGBsIM+DuAsYG4hYwNhBmwN0FjA3ELWBsIMyAu3sBo8nt//iP/1j93u/9XvXQQw9Vv/3bv73st9/4jd+ojjnmmOoZz3hGtf7661f33ntv9YUvfGHZvxfefO1rX6v++I//eEBYTXbpXsBoPvGf//mfVyeccEK16667VjvvvHO1yy67LOtthx12qJ7znOdUP/ZjP1atvvrq1Qte8ILqRS960bJ+J8+/0047VXvssUf1+c9/fjLEDHhWL2D893//9/ClvfKVrwySJEoTEqVsS4MG6623XrX22mtXT3va06p11123+sQnPjEgrCa7dO9gfOYznxmkx4c//OGqbEuHBpdffnl1yimnVEBJQMwFGDfYYIPqoIMOqhROKtvSoYGyhJ/61KeqjTbaqMKjuQDjs5/97OqQQw6ZTE6XswajAFOKU7bxxhtXeFTAOBipy4W7KFDA2EWhcnxmFChgnBmpy426KFDA2EWhcnxmFChgnBmpy426KFDA2EWhcnxmFChgnBmpy426KFDA2EWhcnxmFChgnBmp5/dG//u//1v9z//8T9j8Pd7i8X/913+tPvvZz/5Q0Dsej9fwW3ed8esO8X/vY9NlBGYINq18TWCRKfX973+/+t3f/d3qq1/9avXII49U3/ve9yoS0HHbP/3TP1W///u/H1LGpI4Zn5YkMTo2/Vd/9VfVH/zBH4RruM43v/nN6m//9m+fvKHr/cVf/EX1rW99q7LamdWypAsOsQxJLRg9QM72D//wD9Uf/dEfVfvss08Y9/zZn/3ZrPPjvRB4sb7KJ6m/xP5AD4z/t3/7t/Drf9LLuP9ZZ51V7bbbbpV0N+lhZ5xxRlg8KUq5xx9/vHr5y18ejj3/+c+vNttss5ASB5C33HJLuN61114b+OYatte97nUBwJEM1r8555xzqv3337964xvfWOkP4P/8z//cO69qwfiVr3ylytkknRqE/+mf/umQpvTiF78463z3+p3f+Z3whVIniFnaAgWA8E//9E+DiiWV/uM//iOAwO/VV18dMnFOPvnk6tRTT62uu+66AFqAtZFob3/726tjjz22+vmf//nqZS97WbXaaqsFHgGV45/85CcDiE866aTKdS655JKQmxrpT9DoK9F4v/32C+DXD0jdo89WC8af+ZmfqV7xileElaGsDtW1HXDAAeELfO5znxuyQrbeeuvOc0av6avzBf/iL/5iUAVDqIA+iTaLa8mepy4feOCB6s1vfnMlV/S+++4LYHN/H6xMHEnNQAUcgIN2NIxpEyTY7bffHiTb4YcfHlL7pPhJI3vpS19anXjiidVFF11UffzjH68+97nPBVX/J3/yJxWBEFvM4v/Od74T1L2k3N/6rd8Kklkfxz2HFcVGz4vn5/zWglFmM0C+4Q1vqI466qhBN/c44ogjgoqQJW7qgq9+3huJaM1CHy0VTLp9/etfb6UNEEaTSVYOEEf1S2vttdde1b777hu2vffeO2gyx2V/H3nkkdX1119fPfroowHYTKc6DUUaAmCUigB42223VXfffXcQJE3npfCzFow/8RM/UV1xxRUzWbgxSoBf/uVfrqj3AsYFtnE+qEMSDbCiem5iKnCQpCQhAG+++ebVT/3UTwU1fccddwRHh5onwQCWRCU5edjvfOc7g2YyzYJGtGai44DV1tzzr//6r6uf+7mfC/c6//zzg1PVdV7TNQsYmyizyPt9pGxFjiHvNUqi8ceyX1+eNAFirg4peOGFF4ZzqVDODjDrF50bf5OkJDBwAuq73/3uAMYXvvCFAcQ8deBta8wCnjbHhwQHZGZDnVRtu45jBYxdFJrR8QgqoIlRBQy1vwmIHg2Yvvvd71bnnXdeAMNrX/vaIO3YjDm2t3sBLWf06KOPrnbcccfgFAkZkdJt4ALsL3/5ywGQPHr2a1v/JpIWMDZRZsb7MZQEJKFIszYAxkdzDsZTs1Z+ZfeJE3ap9Hh+3S8QkWxnn312te2221bHHXdcuCbQtz0T4HN+ODpFTddRdhntI304LK95zWvCHG3MbWO+V2MjcjrYem95y1sCEKJUnebV3VswnM0qjvkrv/Ir4SMB8qbmWQE55bmbrlEkYxNlZrgfI0kj6pED8fDDD7eqOf1JxQcffDB4xsJiiidQs3019zDiIprCFnQvAE1pPghB8S57c/xavYHRw/tyiOi2L2j8ARDVFz7P3jQaGJLbaqutgu1HVbc1EojTQWJxNoymYDwe9Nk8lzinKIcPxTOSfF3Nh/Wbv/mbYeCjq+/o8d7AGEU7748XmNoKGBeckFtvvbUyZCeMQ2W3NR+7ENhLXvKSEFYBxBSQtF2z6ZjQDfvRh+IZ2bVd7Utf+lKIaRIwOW1qMPoaf/CDHwTivOtd7wqlM3yxqa2AcWE0haRTz4cT0AUs6njFihVhYELAWf82qUiSUps0ECDri+5xH/A3na//F7/4xeDM/Nqv/VpSjR4Alp9w8MEHp8Ig9JsajAjjK/X1sF2MouR8EQWMC/wCBrYW4DQBQ0/HMdtICmdH6KWroTF1+5GPfCTYpnhGgADylVdeGTRZ0z3tB2LDkUbLFI3qaqSnoUajPDltajAKQ/z6r/969apXvaq68847A4EKGHNYUAXwAVkXEF0VYA3ZUenozD7raq7LAZEoAUykLydJcPyaa67pvIYhv/e+973VnnvuGQpGNQE3Pge/QcKFLK6cNjUYqQgBVvGuxx57LGSHFDDmsGABYKQVidKlogFDUgMbjqpO9VgB8Pjjj6/e9ra3VTfffHMYZpTRYz+AtzWq+jOf+UwY8oupZ22ABP4nnngifDRt1x0/NjUYPZTN18Db+oVf+IWipsep3PE/h0+aFg3TBS52niyb5z3veSHG6P+Upt/HPvaxMLJy6KGHhvKFQjcpmTbAamiQJCXxnANwbc3xrg9r/PypwRgv6OspYIzUyPtlc8s3VDBLgkJb42zIW5Sux7tNAZPr6Ue9b7nllkHdCr10OT7xOfT7wz/8w3Ae5xSw2aFtzfEuiTt+fgHjOEUW4X9SR3YOp6QrxggIN910U5CMJCT1ntIErC+77LKg3jkWbMg2VTt6TWAkaORASsBwzzYwui7wc3xyWgFjDrUG6svWloYlSdm8lraGyffcc0+QcOpfdql11+I5y8TnUNx1110hxeyqq64KgfMUVUrriR1KSePwdElU/W+88cYQKG97l/FjBYzjFFmE/6V/CY2ddtppAThtj0D1maax3XbbVTF/sKk/uy06HxKY3/e+9wUzQKqY7B5JFSmS1QcgPW333XdP8qYlVbzjHe8IyRtNz1a3v3cwymsr3nQdqZv3AYygN7XWJakAjF0pgUGWDqna1FyLVxt54jz7pHuJUXKauiQrlevZSG51N1PijMDItuRk5bRewcjIFRg988wzk5+B7YEJADyvmd4YDmS2FDuO3UiKSqqgdtGw7jzXs6qBKQERiPqRdBwYk+B8CG2NJCZBpZPhq1BQV1t0yYggjGThCSGE1FbAuBD0joCsA9U4LQFIupnRLtNIjcjUgcq10NexUYlrv/+F4wC2rRnUEM80yY69SEp2NdeGAatf5LTeJGN8QV+Fl0xtBYwLYRcfsnhjHajGaQlA1Kvpo9S12XqclBQgj1+r7X9S0cR+jhXnR2hoFNRN53oOGOgyAcbP7w2M4xdO/b+AsapMtueMGB0h5VIahptoJRAtiG0eSgqQU64d+5CKpjNsuummQdIZaRuyFTAOSd3Ea+cEvUcvSZqacyKQ/Z73vCeAmuSaVkISEILrH/jAB8I0VlNexT9zNJ5ncJ2cVsCYQ62B+uYEvUcfAfAM6Sk7Yp67oDYpK1zTZQuOXmf0b9JVnoE4Ial72GGHhSxyTk8qyIEQeFMyikbvXcA4So1F+tv85de//vUh/y8lC2f0MYGHimbXbb/99tUFF1wQAMpeY/OlAChKMfa+oLtUM8ON4opSz0jElOvE59KfpAbmnFbAmEOtgfqyxWR4y6YhgXJaBBJHw6QsqWXKxLiWKayA0SYlnQ/QbFXZQFQytf/qV786xCPbEm+bnhOofRQyi3JaLRitoHTppZeG+J8vbMhNjNEIhMJDviT2U9+GeA5BFqMvtQY0gJhrZ8XndT6V/au/+qtBZRtHBk4VJgDVdBBSjwq2iTuKGQqai1VKhjWNAQ9OP/30kKUjpa0NyPHe47/AKOhNuua0WjAqDCRGJFnWmGbK5oV4d15eZauUc/RxDzlyhqsEvb/xjW/MHRhzGNbWF5AFxE0TIOGEfahuWdq8Yjal8ewPfvCDYWjQkJ2iWyZ1GXeW/ocfHCPXylHNo8/lw7j44ovD/Uf3d/1dC0aVqtTbUc8vZeP6W5POqp22Zz3rWUnnxWs7f5NNNgmZyKL9bJ3SpqMAqSYuSDhQ2wLk6Pz0pz+9+tEf/dFQiUzVCGPUhgWNdztnUsk8+rSuYXRHdlFOqwWj1CQ2jHy5lE203dfm5RSiZPimnDfax3wMJd8mVQ05L73U+gpYc2KoUzZaH4169VHzrNmkVDI+McEIG6MpPF5S0KgKaTaNNBx9ZhLVvUnpnFYLRg+Ws3mZUrk2h+wr9+UNM4uEaFKD3itfofs//CwLWXbTae57TBpnzCHcLMFIMoqB5kYGaiVjzkvq60VlhzCUS4H5XOpVwXNNzfTOv/rCGbMEIyAqbMrUy2m1YMwN5bA7eMHmTXNeBGBzr0HVx5GDSb24nBdfSn2l3kl64M12qWm2oNAX2zqHxngkyrHhhhsGHt1www1Z57tXKo8A38QtoaKcVgtGjgUvTKjGC3Rt+ova77LLLtU666wTPLeuc+Jx94j3kWPnhSeJbeW89FLrCyikiCG4LqNfDE/EQSgtl0cC0cJ2eCT1LPKg63eUR5bwoH7beNRrnHGttdYKX4/wTurmi/OSa665ZvhNPU8/qt0mUMurnLegd87HYZBAGRmhNFooh848afyxWQsm59zII1njpHcbj3oFo/CMm0qUVRY3dRPecY7f1HP0N45pWYd5HYHJAaMwjeKgajJKOZsVj9TZoflMqe0CI6AKsMtEz2m1atpX8P73vz/YJey4ITe2j6TSU045JQxjzeNwYIwHogXjv61FMCogL9vbOUPyx7XdQ+iOL0BIMSvaJKN4JQ1nFmNOqwUj8V1WO8gh43R9Bb1NdGKPddmMEYw/+ZM/GaaP9jFi0vX07kFgSJ5IAWPX9ZqOFzA2UWaG+0UipJBhdlcKWQHjgIzx1c377MCcoPdyACNPm3qnznNakYw51BqoLztZjFGBTaldbW05gJHdawkPzlVOK2DModZAfY1Nyz00KR/Y2tpyAGOvoZ1JHJiYqeFBROBTW1HTC8Opgv2A1pU+Nw0Yp+FRjgOzqGBEQB4h28dojOTO1FbAmEqphX6TgjHySGkTycymJKS2XG+aMBKXtEhmTptaTTNWza81MC6J09p1KqKmtgLGp8ooo0XXuPwkYMQjTqLMelndMurFKFNbLhgBn73IBs5pU4ORerEyp7CErGF1o0vhpxwWDK+maS2jYuo/mmukNrfJV6ktF4w+KEHxrpjp+P2nBqNB809/+tNhRU5fm1SoAsZxMrf/b709k/EBhZZpa5NIRmEWalNChOU9gJIASW25YEy97ni/qcHoQdkIJKTgbanpPU7i7v+HjjOO8sgoD/U5NBjds23IsI4qU4MxXtSNS03vSI2836HBGJ8Gj0y8GhqM1PSiBr0LGCPL83+jRhk66D0rMLqPMs1Ko+S0IhlzqDVQX9VlpdFJDZNR3dYmsRnj9WYFRnHG3ipKTBL0LpIxsjz/1/AZBvI+2VptbbmAcdHLKBebsQ1GzcfYWDbxQL9tbbmAcUkUmC/edBuU6o9FIK4qYCTpFQw47rjj6l+4YW9vNqOou3jZW9/61mAvNNzvh3ZTS/OeQiZWGwsxdY3rTyMZ8UjJEwmyQjypDY9yxqZ9XN6jy/4dv39vYPQA3HnTLnPHPecdjFL6Vf6y0GTXVNVpwIhHphCYEtAVXB8FSi4YR8/N+bs3MLopNUNE21JbkYxVKAOYunbgNGCchkc5kjHeB29zWq9gzLlx7FvAuFBRwri+Ybqu5dqmBWOke85vrmTUX7hKJbKcVsCYQ62B+lKbEmutWrAqzIFhL6rPqAxfTitgzKHWQH3ZbxYXt5JVV7Gk5SAZFz3oPSmfipquQqCbNAFE9GhrywWMvQa9ldvliPDAhtzcA4GlnVk+Yh4n8beBb/zYKBhl1M+KR2zAV73qVUnzpn1YCj8pV5PTGtW0ZEzi1ssOuXlwBc+V6ihg7GbdKBgt0zYrHlkE4KCDDkoCo6iKqrhimjmtFoxrrLFGyLiwLvF73/vepM1Av/42f6eep78K/eqyKIgug8U49zw1sUVSTva1vNC2JiaLXkrQKAkzKx6de+65YY1rS/121drx/MwNgian1YJR5Xu19fbaa69q77337txMNVDHWzEila6sM5xyXuzjfCJdrM3yESTxPDVj+uYPWQOalmhran4rPYNeuTzi3aoWh0eW7I30T/mNPDK/KaUmUNs7NB2rBSMRm7MR4Q8//HAAr+LlVuDMOV9fw2G8ymgDNT3wqrg/J7mWxDHSJQSUQ2M8slDReIH5nGuk8oiPQbv1Mgcm10Z0UxINCL2syVm519Afob3IvLUcMKLP6EhXKp3xSPgoai/TVVPPHe2XwiNj4OZF8ahzWq1kzLmAvmyDUtM7l2pP9Tc2raLEG97whs6KEk+dlfcXHs1qtQP36m3edG4oh0dHDcQC8wcffPBE4aA88q46vZknSkibJEUFp7RJeDQOxtxr6J/S4KG35dqI4pxNsFamzigYc86Pfamf0ropABRoFemW8otHwE5N88QtPJVy3nifFB71CkYByxUrViRvQjnmPPDQfvzHfzz85pyvr0q57BihCwQorZ4CJKcEBBUbcmiMR0wBYTs8srZgzvmRR6pSdE2P4Lwooy1IntNqbUZfznbbbRfKYAgfdG3KZQjtqK1ie9GLXtR5Trymc4Uctt566+CNC3MwgOepYZ5wCXXd9e6qQ4gtbrHFFmGRSvSLtGz77YNHluy1iheB0fachAlN+aUvfSmLjbVgVEX/oosuCk6JPLYhN2vayVqRoj6vBeaFaVR7sPAjULa1OAJj4U+JFRzHIfnj2nhkXUPr/IgFd9X0bnv+tmO1YBQYNRzIK/IFDLm5x7wPBxp1MhWAWkstFkoyGg6cFY84qOZ1l5rebZ/TKnAsJ84YJeNSLjDPweIwedacVisZJ5k3nXPT0b7si3mfAzOJZFzKYBQkf/DBB6vLL798lNWdfxcwdpJo+A6PP/549Uu/9EvVm970pvBhtt1xOUjGXkM7RTK2waH/Y+w+2TpdXqo7FzD2T/8nr1jU9JOkSPpjOYDRx9XbcOAkkhGoGK0CosR0aitgHL6McuTFKI8AJrU5T4gndYUs0Zdrr702LLSUeg/9erEZPazqAZJDL7zwwjDUlPoQBYxV+HgFvIW4uhKLJ5WM6CxgfvXVV4fkXB58assFI2+6txSyHMnopuZHAKJk3J133rk666yzUt8zDP3Nuzct/e6EE04IDgxQtrVJwIhHguOKMRkdkygrMSO15YIx9brj/aaWjDKP77zzzjBt4MQTTwy/pab3OJnb/x86zmiagDWqFQqguWSJD1lGmWQU3skx11BoajAavjJUZHkuK4OWKmTtwKs7OjQYqWdDh4899lgYtTGxakgwyuxxz5yaS72AkQiPoYlYDrhIxjrINe+LQe+hVlUd5dEsCszDgywhuQY5bWrJGG/GLinFQiM18n7NQ7nyyitDGl3X7MBJbMb4NHg0iwLzix70LmCMLM//jZJLaKwreXW5gFF+65ZbbplFjCIZs8g1TGcGf9y67rBcwLioQe8iGbtg1HwcEKN0XBUkI09aYi3TI6cVyZhDrYH6+pB5np///OfDCBZwNrXlIBmB0SCIUZucVsCYQ62B+sqcVqlBrSHTVknJprYcwCj2bI7OZZdd1vQatft7A6PxSF+3wLdaMKkN4ed9BIYHff7551fPfe5zw8gIR6apTQNGPIpLMQ9ZYN5ojzCVki05rTcwsnWIZoFvcbPUVsBYhQQTU0c33njj6qMf/WgIGDfRbxow4pEP3+xC4aTUhkc5iRLm85gAliOUPEtvYEx9sfF+BYwLhfm/9a1vhZmVpgkDXFObBoxN1+zanwNGgFcd7cADD6xuvfXWrkuvdLyAcSVyLN4/VLNaOJImODRNbamDkfPCVpSUwf7NaQWMOdQasC+JYuQCM/3d1JY6GD03c032kdzWnFbAmEOtGfXlaGCk6hHAOdqWIhiFojyn524LS42+R93fBYx1VFnkfaTK7bffHhwNUma0LUUwkuSydDy3vycFZAHjKKeXyN8WJrIujKwXC0LyZCODlxIYAU9MUf0da9gou9JVh6eNxLVgVH2WAWodQNMoh9zcQzhIISL1espqB1UocaJ83R577BESYa1qz57EfGAUMhEGIj1nxSM1x2WIx/Im0sSEiTybZF2lTyRZx+dsA13TsVowrr322tWOO+5Y7b///smbpcZibWjF4lPP3W+//UJ2+POf//wQm1J3h+0xz40UxGzJsIcddliQkgLj7DIAAMb1118/TCFAaxWD0XGU5vhhf9yUK7RFHgGP/+Nxv84ZvYZr6qMvwG266aYhedoH4fl8DEaNHJe869mmabVgpCKOOuqo6uijj66OOeaYzk3fww8/PDwsIEsdSjlPH/eI9znvvPNCMFZca94bQMYx629+85sBiPaxIa3RY2UIVceA8YADDgggibQ08nHIIYcEIDkOUOrk+F133XUrPGICiAXapw8g4qHquZF3pinICgc2UlFf0xeoYh+GukD33ntvyGP1sUzLt1owmmCVs4mNiep7YC/r5XLO15dd5IvzktE+mndAen/0GPVS42oHSgiqRLb55psHqaUIlOJMhuKobhKVJDO5jkp//etfH0C83nrrVeuss051zjnnVLRR7OM6ppdKkI68M19m++23DwVG3Qtg8TnyyC+17KNhQkzbasGYe1EiGxF8OWo7+ipLG4YCmG9cGVCsUa2UoAWdABBQBc/9vu997wsSjpZTOcw0AM4Q/lDxRnqMlJCCjusna0h5Pvcg5ahe17ag/amnnhom5hspGkpYFDAOg5mZXBVojDHHfABAIdUIB8eAUriFmrc0ivxCtTeBUZVgwKVyee/sU84jm/073/lO2O8aNv3Yg+Z1+wXUIQBZwDgT2Ex3E2oaqADFb2z+JrE4mzvttFOIRpx99tnBrgQY6hNA2YLms7PllVCmqj/xiU8E1UrVmvO+5557BodIP/PfRVAAEeiA8cwzzwz7jz322BDCYRZM67DE94i/tWDMDeWwM2T2CkWwR9iOuddgd/pC+7I/4gsu51+AwnBTWc24FFahjqNUApJHHnkkAAu47rjjjqDCjdzo4/w4TVUI5uSTT65WX331YNffcMMNAbSmGuMVlSyxwXU4JeZax6iG3wceeODJ9R2toMaRkYfZZ6sFoy8juvqM1q5NX0Bkj6y55prBsO46Z/Q4W9P/SsJREb7WeW9RIlnVSjqWSrUCy8AXwdhEI84EVc3D5Ria037XXXc9GRISR7YW4D333BPyJ4ERaIE7Oifj144BbgLDgkMEkOtrngdgCZKuZxu/7uj/tWBca621QjqTmJOwQdemX4wXxlBC1znxuHOdY6UEMSu5kF5q3hvmC+Mcf/zxIUlVTA+wgKytOY+044womYK+1LPiojxwv4Atkdf/1nkkTISDSEQ2aBP9XRtYPQPw+R/4SGLlUmg3+ycFZC0YfTm8NSlAbjDk5h6WgrUsRBmBeQpmGAoUHBLaghTC6KYWwcsRYd+pqSMW6aMXv+XA+NDZnTZ/22fxIPFGQW12JxuUPZhaRN59SdYYnOcE+RgmAWQtGHMKPzURJ3V/tIvYRNTRvA8HRg8WkzVMbWOsY/qyLdl8gCV+aImM2267LUhTKrhO2jmXNy2cQ/WedNJJwdERTP/IRz4SwnVUd1tzb9cHasuuCAX5eLokeN01CxjrqLJI+zCWI2ipi+jJdj2KczDe+t5AaP0e9bSFYXzoqQ0wAY+jAoy0o9ikQLp7dDUOj3iksBEnyP+5rYAxl2ID9Y8q2eLiNtKqC0wARCqJH+6yyy7VEUccEWw3IR/XczynAR1JKS4pGG705Z3vfGcAZJuJ4B6OszdN3lcIjB2Z2woYcyk2UH824Y033hhihpauY3d1SSR9OB1sPQD+8pe/HALdXed1vQJJy09gB3IqFRgdDfU0nc+58fV+uEEAACAASURBVB6k+iQRkQLGJsrOeD9JyN4zlMq56JJqjht5kcjwwhe+sLrvvvsCgPt8bPY7B4gzxNmJoZyUe/gguiT7+HUKGMcpsgj/A5axfeExGTld9pb+pI9kVqrUopHOmVYijr86VS9HERgFzDkmKffQh/2ZO0LTGxiJZTcXC8uJzBdvegECmMdxYe91eaLsM+AVHyRNhX+As+8G9J7JECBP2ezFFFtQH4kYHKCcNjUYPbCbi8ybiG5xHTZGaitgTKXUU/0Al9MiLmuYD3jbJBYeAbDz0Nv/+pN89vltakAu7CNwDlxdaxu6DnUux9XIWk6bGowkorImynNsttlmIaJfKtfmsCCvLyBhtkUvbSnL6AKg4TuDC7xl/wMgvgnltKlf9yOteeuGawXMu5p7iDdS7zltajBKUxJsfc1rXlNdeuml1cEHHxwG9VMfokjGKgADHYVpurxQxzk4nBZ1jcQBuxopyMHhHcvikcTsGnjVVcHCtWk+halMWTA6A6BtjbSNtYPa+o0fmxqMbuwLe+ihh8IgvsySIhnHydz+P5tPfM4oxvjU1PEzqU2TtSxEDkikVlcDHsOuxp+dIyhuApz/SUySrK0xAyRVyNaRB+mDaAMkqauqBJs2p00NxngzD+DFymoHkSLpvzmrHZBSNJEEh+uvv74TSPEpxCR56mKS5rlQ8UJDXUB0PntTmIeNyoMngNpsVMdcV7gqpxUw5lBroL45YKTOr7vuupB1Y+wZMFIaQMmFlB0l31SwnJRtA1W8LknoXAm4pDegMa/amut2mRzj5xcwjlNkEf6nUahMdrcx5bYGCBJjpYAZAyYpUxp71BwYaWMC2VR1ChBdG6g8o8we8+ndswuMKc803qeAcZwii/A/dQZY1G7XKAdJKBBNTVO71G9Xc44EW2A31swRUQfS/hRQMcFMAmMzXnHFFcHhagOyY0VNd3FlFTjOmeDRcmBM5ucZdzWeM2l42mmnhQC5eTI8a4kNXQF216bOb7rpphCqEXNsc170B16zE4E+pxXJmEOtJdCXJBMXNAlLzqJQTVMjoXjbhvJsnBAqVha4MXA1ctigXU0f3rfhSskYXQ14fSjS2XJab2BkICMMAvnyUhviGkac5+RaNCChUtQmqTQ6wmFmH9DVSSv7gc/Ee2lh/o4AVdvbPsBpa55NBg/wi2u2gT9exzU5OuzanNYbGBm5xL4kT1nCqa2AcaG4polW7DKA7GqAGxMY0Hsoh8JzRIeJjWoFgxSzwPMt6qJEvkyA9CBshtRWwFiFITblR4yIpMTm0EwyCodE7E/YBSD7bnhKekra5bwYekzhreczbCh8lNN6k4w5Nx3tW8BYhXnRJtqbrku7dDUgAQret0n37EFZPEylPhtzQHqacJCEXxlZ1HxX83yehVTNaQWMOdQaqK8ZfaQPj1f2U2ozK0/yAs8aMHPnvTTdB+BoONNjzYeXwOteQ0jf0WcoYBylxiL9TaUpvMTDTVHT8TGZRcacd9111+BgCGSzOUmmaRogyuxmAph2II+RlJv2ul3PVMDYRaEZHJccIWQSwZR6S+AAEuepAsKuEwin6ru85Lp7uJ5QkLxUoy3ASOKKdgB+atNXpdsPfvCDqaeEfgWMWeQapjO1yMYikVJsstGn0J80lMkDQHIIJThT/aRsl6cNgO5ruJCUFR8kDW0SMlLtxNFncr2LLroo2LOj+7v+rgXjhhtuGFDtoog05OYLZutIxkSAeZ3EDxS2SRuHhrrnlSv8ydbjfAgXyc7mjJCi6G0DUkOJpJ6wkhEW86W32WabYLsKjJOSuR+H53f93uKMSqZBNg9Nrt2Qm3sYrjIBXGnfeQQjhlNtPvpJARklHOCJQQr7mCpgFMTIiamskhzkJVrbT15jTCXjkau/A8DGrCXsApRIxyStVzAqb+IlgCOK7LZf/RjRZqo5T7S+rf/oMeeydYQPjGXKDsGUeWo0gzFfKWEpiQ9ttAEg1/CRczzU+VbPG9BkhxsVAbxYaIsHz3kCYPFKswxpxGma81esWBHumXOdWjV9wQUXVDmbwkLUrCi9YpRCDTnn6yubxMiNYO6kX2TOiy+lvtGbVvKuK4Us9blJSqqbqjWWLQCNRyrMqdFIE0UAojm1PYlKrnseUt5wI5szp9WCMecC+voSfImlpncu5Rb65yTXTnaHBR5xchSbV0dTytpSawWMS4AjBYwLTChgXAJgNLqhKKhiS9TqEI32mpVkZCKw+3sZDswN5bipNCOzwTbYYIPq1a9+dXY4iJ3BVpzUmxyCgbO6Ju8TCNmLXYkI6DPqfafyCo84NM95znMCj8zySz039kvlET5yRN0vp9VKRoHOnI2BHBclUtdPWeSc8/U1ajCvixJFgKV8jAABWMawc2iMR2KJhAUecRZzzs/hESncWwqZEIBQjSBoyiZUI1a10UYbVQLmvOqU82If57ufVHijAAheWj0FhG3kFaLXJDwStsMjMchI/5TfyCNTFwTQ23jUa5xxtdVWCwWFhGxE0lM3VQTilnqOe5xxxhlhKAtx5zHoTZJgMM1AJbY1feJClmzMWfFIrW+jM7KLhILazAlg9Iwq6ea0WjXt6zHgDv1UyJCbeyCwL25ea3pzYKT0AxdatDXHxWStWiAZYVY8Uo3MxH9Lu3WBEVAFvc2zzmmNYDQlcRbBZ/eY9zkwhkNV4sDsripfo2CUeT0rHhkSTgUjB4s5kZObCbQFjDmf7kB9c+KMiwVGDowoSYpknJRMBYyTUq7H89jJJKMx5KUqGXPBGMNPOWQqYMyh1kB9qUBVu6zH11WFbDlIRkAUfsodZy9gHAhgOZflTQNhl2PgmssBjByYD3zgAyEik0OH3sDI4+bZCU34TW3FgUml1EK/acA4DY9y1HSMM4o357TewEg0+7qluueMrxYw5rBrOsmIR3iDR13mwOhT4dEkYJx5RQlfm1osyl5YQFGCrEUwU1sB40JFCYU7v/KVr3RWlJhEMuKRUIuVT2WAy/w2HSG1TQLGRam1IylTcqgaO4KcZpSVMsqpbF7oJ+htEpXiSmKubW0SMOKROS3mP5sjY2jvs5/9bNttVjqWC0ammqJS55xzzkrX6fpnajWNOEZrFLuUOWx8uYCxi+wrHx86zihJAtiVQL7jjjtCEvSQYCSJOTGkcU6bGoy+gmiHIGopMJ9D/oW+Q4MRj4RZeOuKhpKQQ4LRWwEkGzWnTQ3GeFMeFHVdCsznkH+hr9w/M/Vola7Y3CRqepRHigUIrg8NRkDMiaqgxNRgjKQnlhG1gDFSJP0XAO++++5QyUH2TlubBIzxenjESRoajIDI++aU5bQCxhxqLYG+ywGMgvjs09122y2LYgWMWeRa/M7LAYxMNuE9c7NzWgFjDrUG6it0QpqklFFeLmDsrbyJ5NrcfMZiM06OVKMhgtApVciWCxglAJu+ktOKZMyh1kB9RSGG9KbjY8/KgSHpObNKtuS03sDoAeTiKXh+7bXXJj+D8+Y901uc8bWvfW0oo9yVHT2NZERroz3KyfgAUpvzcsamFy3oHV8oPoBxasNPqa2AsQqT0FQJO/DAAwdNrp2GRzlgTOX9eL/eJOP4hVP/L2CswooCanMbvRoi6J3Ki6Z+uZKx6Tpd+wsYuyg0g+PGcJWjo66FRdraNGq67bptx3LBaOTFknISbHNaAWMOtQbqa8QCw40hU6VtbTmAUZjq4osvDkUG2t5l/FgB4zhFFuF/AIxb1+2XAxhjpvfMk2u7iNd1vNiMVZCKMejdlekyd2BUTNJsNcFY3vGQm3uYHWeVJ0mf81jeRDhHISY1dFITJRSRlzA7Kx6xaZVclgjTNXFMPPOqq66qrPqV02rVtALzgrBGYVw0ZbvyyitDkq1E25zz9LU2sbAGMKqu4GXmqXlnk+NNku9alEhMVoWvTTbZJEzzyKH1NDyS+KD2uudU97uNR7SdqnKPPvpoFhtrwahkGumoll/KFquPrbnmmqFe9DrrrJN0Xry28/1tYR0LJzLk56nlJNdKZAYMYMzlkXJ4a6yxRuARgRPpn/IbeXTUUUeFQYoheFQLRlX3padboiFlUx+a9LQgzrrrrhvmwaScF/u4lykLJgwJc3TZTasaUHPASCJRmXfddVc2j4y8POtZzwo8evvb357E23EePfTQQyGpYwge1YJRNYCczddKoikSuv7664e09pzz9TVqw4jvCm2sakD0PjlllNFHHA+9cmiMRyZJSYLBI4VDc87P4RGg6t8VwB/nZS0Yxzt1/Q9EZbWDLio1HxcKARbMa7PFmq/QfQSPZlXTmwqn7U4//fTuBxvpUcA4QozF+pO0I00Y/kNphlmC0cfV27zp3FAOD0/KUFTTPOPcaxDrXmIIW2SxQDbEfdGH5EGvHBrjETszqukbb7wx63z3SuVRr0FvS7NaBFGYJmW7/PLLQzVVZXPXXnvtUN875bzYx72EKDhCiDZvgCS1Usso66uYP4cxl0diuSIleCQxI9I/5TfySI5il9CIkrGXMspqentg7n/qxot2nk2IJ/U8/RCIlyfOKM9uiLDBEFKqr2tGB0ZVDiMsbY1tKc4oTIPmOXSelkfuJc7oGdt4xO4VwN9///3bXuWHjtXajB5aPOmaa64JibKSZVM2owi2nPP09eCmT1rUcl6D3kY2Usoo0xxS+sUGzz333Cxa4+GkPLr00ktD0NtzdgW9aTYhuq5E4XE01oLRV+fmvkLqY8jNPXjiJ5100twOB+bEGePYtOHA++67b2Y8Eroj6VKGA8dBlvp/LRgnmZCVesPxfiVRograQEGmgw8+uHM4MILRagezLDCfm+lNOuJtTitgzKHWQH1/8IMfVEY2zA7smrKxHMAIiN5DQkVOK2DModZAfY2omDMtfNIlTZYDGDkwvG+JHzmtgDGHWkug73IAo9COcXBLwuW0AsYcai2BvssFjItaUQKf2AriTzml0IoDUwWPWN1EybJD24yT8ijHgSEZF62iBECxd6yIKuXImnaprYCxCnR7y1veEhKaSb62NqlkjDwybPvxj3+8shZganNuDhgJIx+XkbycNrWa9qWJQwLgkUceWe2yyy5ZtZwLGKswRVWK/r777hsypNsYOAkY8Uiw/Oabbw6x3Je97GXVAw880HablY7lgjGmuXHKctrUYCQRFbr0gqoiSJbISR0qYBwejHhEbcqkV6rupS99afW5z30uGSe5YHThmImUfJM+KteycZTkfc973lPdf//9pcB8DvX/vy/VqUC/ZTG6ElInkYyG5swzkk0vc+eVr3zloGWUF00yxnQmRIoLMpbVDvIQKTjsQ6ZhmDxtbRIw4hHpSFUbtRm6jDJJ+vDDD1e33HJL26v80LGp1XS8okCnL9zYZQFjpEr/v5OAMT4FHs2ipveietNetoAxsnzY3+UCRkHvrbbaKosYRTJmkWuYztSapNlSRrmGvpNk7RTJWEPIxF0SJQS8P/OZzwyydmB8jFmpaR+WBOAddtgh3jrpt0jGJDIN24mtrYLHIYccMmgK2azASNIrWWN6RE4rYMyh1kB9TTsQ2lEE4Xvf+17rDMHlYDMK7cQoSw7JegOjm3/729+ujj322MogeWrzFQk58MBf/OIXz2XhJ/V1LDRpdQDTLtCkqU0DRjyyapUKublDtjnDgTHg7Ten9QZGQ06Cq9ad/u53v5v8DAWMVaCbGZZGr4ReqNOmNg0Y8UjVMlMIuoLro/fHoxwwGggR18xJmHG/3sDoK/DQCNlGzNGX9HcBYxWYJvBtKV6MBJqmNg0Yp+FRDhg/9rGPhcliFs3Mab2BMeemo30LGBeokarapgHjKN1z/k6VjD4iH5NhTYkf6nrntALGHGrNoC/Gs+2ouDqbaymDkUY0rLnTTjtVb3vb24IPkUOyAsYcas2gL1vuox/9aPCq62yupQxG9igQKioKlKRkTitgzKHWDPpKTpbXiKnsNAHk0baUwWhM2hqIsoM8e5vtO/pO8e8CxkiJJfIrEnHWWWdV6tRI+yIpR5m61MAYnSLP6G8mBlD6zW0FjLkUG7g/pgqCH3HEESHRQBrWqHRcSmAEPqpYGZOcCEoTCWvBuPrqq4eY1ymnnFKdeuqpg27u8da3vjWs2r7rrrvOZdB7lDkYrPTcY489FuriKP3CqYkNGGVrK0Fj8ctZ8ejNb35ztfXWW4ePRBjKeLrhvtNOOy08h/zFSaRhfC+/tWA0ErDbbrtVe+yxR9L2kpe8JBitip4rRG6+bOq5+jnf/Q477LAwOanOcB996FX976juJNqSiv7XgMAKAqZ1oPELXvCCMKcl0hodFc9CSx+2X/+bZuCY+UkKRkmEcb4+u++++0rXcC0jYc6NW+yjP+FkxIgJIUhv3wknnBA852n5VgtGX2XO9sgjj4QiRF7CSgd77rln1vnuZRiMvTRK/FUddDnvRzq+//3vr/bZZ59QqcHw4SWXXBJieZFXRm+uu+660A9YrN136623hqxrPFIDU+lBmo+k00cFOOWVv/71rweeATsHxIiQtYDc0zVJQfcRmI9FoAwrWs4jButz3qeuby0Y4yhK6q9hQHYOQlEfSrulnjvarym2Vvfg87aPLQkwcT2WLbbYolIsKpYQREerIFDdpN5mm21WbbvttpVVDUgyPFLok+Z6xjOeEepv6rPddtuF+ttMA4JAeMaa4VSyeygwpRIxQWGIjyrWz32ZEPq796iTNSlvasGYezEPVwrM51Itr3+0JS0wDwiWKTGfhfMAEDaJKqTh+eefX5133nmhrrZQEY+cilf0fcMNNwzFXA899NDQR97hV7/61WADuoZ+Jm3Fa0h6IVFdg7MSBQaPuW8tVsCYh4lF6Q2I1DQJFMHglzOjAKiiobZzzjkn/C/Gp6Cn4wBK3Z599tlBkjKjVAqmeh1XHxMYTWUFYP0AkComUWVU6SeIbRYoCWn/JIkQXcQrYOyi0BI4DogAwZ4bnT0IcIqsWr3Utv3224c1GPV1DpUqi0o1sG222Sao6Kc97Wmh/LL66Rr1Sn1zUqhm1/E36RtHUPyqeEHtm9fCVpSVzqPus9WCUSHynO3EE08MZZc33XTTUNP7ec97Xtb57mXEga1CDSFkaQtAQQ+lpmWBcwyp5mifUZNKyqjraJOjKGvcfn38UuNilejr/Kc//emBR5J5lTkBOnXUqX1VJlxHrUgqm/TV/HKObrjhhqC++QYcG6q7z1YLRkau8A433wt0bfopDm/Og/OEELrOicfjuQzpl7/85YGY08ar+iTQYl2LamaXWU8FbW28X2oyglEfQNEvbiZ1RYeS9DvmmGNCWEfyAhqTfISFER5hGXxQlgbgqWs1eJxPILi+Fp+FJDSdQNlnPkKU0p7HfW3xnEnoVgtGBeYNSXHnBTOH3NzDF+lLpR7mcYnfOsZhMGaz46hiEpH6bfpQgYBNCSwSLZRkpnZNZaBWzzzzzODckIZAyilhZ6I7oAOo8icAb+oDcKdoKPdlP8YQUsoMx7r3ta8WjDwu8ScX9oJDbu7BIBZMRZQCxqdYBQwcDB5uBEeT5AFScUDqXDiGlrE+IHpabpdUE75h/6G5XxKQ3UnVq2ax9957B5tQvFgtHqo6SuGnnmrlvzwjNa/4vMC6j8Z1J2m1YJxkquokN3eOl5n3OTCjtBtdhQrw0MfW1IAFsIRw1NDxQQvL0GbsRdcD1CYQOx/QgV6ccsWKFcE8Ayyeumu0AdJ1gZt3Tu1LrB11fpqeu25/AWMdVRZhH6bSQJwEpeswuA0EHtE5wMazZfuRaNZ5oaqdn9vcj6QUwlFVju1vhIWwaPsg3If0ttIWb5uZQKrmtgLGXIoN1J/04pxQlQozkUjRm226JYAI90hmNQYNlOy3LhA3XS/uJykNHwI4O97wIOnbJF2d5xgA3nvvveFj8JHktgLGXIoN1B8jlRUkjYyUkGxtzPcYbL2jjz46eMakaQyLdZ3X9QrADJDAzamh/gXPAbKt+Xh8DEJKXZK07joFjHVUmfE+4AEkqvH4448Pox9t0k1/Kp1K5i2LfAi12Ndn84Fcf/31Idh98cUXB0coFej65QKyNzAini/CF5VDFA887w4M2lHRChkYF+ZMtDU0Y6MZWQFg3uwkarHtHvGYERwViZkCZvs1hZZif7/eh+2ZUzfceb2A0c2JZ9F7oyliWKmtgHGBUlQcSUQ9d9mKPvrbb789qHSJEYCYK4VS+YOvYpPikO5FcHQ1oR0rxJ5xxhldXVc6PjUYfSm8N+L8gAMOCAavYGpqK2B8ilJUW5cadByzBavRWy4iYdB2HhqTnmKAEbgAbejQYpjivE3n+zCYAMwBSbRSBbuaYL0yN/vtt19X15WOTw1GLyfGRF0AIWO3VK5dicad/wATpjNv/N3WAIszsfPOO4fkBU5MV3NtoDUSE4fx2KgWQJcPQJ02gdG1SUf5B8Bl3Lqr6S+P0tBwTpsajL4CY5oG2oUDvHABYw4LquClAhVJ1WVvk2jMIfE8uYiGCFOakRg25tVXXx1GaqSbmRJrOBZ42pp78tZ5+vfcc08rcF2HqSENjWrPaVOD0VfHaTHc5IVLTe8c8i/0BcTjjjsuZD51gQujjbZg9FVXXfVkskLXXV3XNAWhGpO4zDciLVMC2j4QEtEIi4WGuiQ4TDAJcnwHzz81GCMRPKAvu4AxUiT915iy6QLUoGB3W2MWsc9l30hO6Ir9xWsBsTSwmDzBAWpLvIjn+QUuvJVhpVa3e7Y5TFS++3V9WKP38HcB4zhFFuH/HDBSqYYMgfG2224LTE95ZOAgCal3IzwqhLXZiaPXBEbj1kZkqN/oBI326ePvAsY+qDjlNXi6JldJ++LZtjVSiVQz6coYMGB0NU4RySaJQXaUKajimUCWAkgREx8MNS2pllnW5Wh1PVPd8QLGOqrMeB91JqAsQaELXIDAWaRujYp0BciBTeBa/Nf0VmPZPGNTVQXOuxwmpODAGKIU+DZOTUW3gdhxCbjOyWkFjDnUGqgv5gFFisSJKlPYxNChUE1TI73EJHnOr3vd60ISs8A6W1MIzgoLXeB3bdJY4QDed0rNReCNqWhNz1a3v4CxjipLeB+JBFC8YfPTVf1qagDOCxaAliwLeAAq2VbOo4n6XZOq3M/QnqwgZWjkKnY1HxXbkl2b03oDI7tCMNYsMi+a2kiFMjadHvRGV86IsA4b7kMf+lBjqAXwAJIqFw9Ga80+jhAgdo01AxbVzCwQGury9l1/0cHoRX2xhgZ9eamtgLEKIRB5gGysFLUJQOapCAWp9kBVA0DfjVQ0OkOyGvGJ0rXrPtS0uTRimjmtN8mYc9PRvgWMVfB0LUpE9aZM/wQS0pFdpvgTiUWV9u3hxpEX49KSHmi+lHuwaxUBkA+Z0woYc6g1UF9hE/UYTWpKUYMeAyCdx26kQjF+0olQTa/F8ybdhIJ4xzRfSvNsAJkrrQsYU6g7cB+MtjoAbzXHxAE+qtPUALMCv/CFLzzppEzzyCSi2CdJLdAtEYbk7bIvp7mncwsYp6VgD+cb3TDZ3lAqpqc2EohzYkRGDJD9KCUsOiaO5zQqmM0KiJ5FuZRLL7002KQ5QHRfTlKupC5gzOHWQH2pMwBiL2JiTgMgcUAjI2w78UfJsBzJ6D2nXA+AgIcTRTUrVcMmVXsxxU4cvQcVLTDvmXJaAWMOtQbqi9kkDyDmMh6InEOi8sgNKZJo1L7hQmpfWKdOsjmXIyS3EQiVOeE1m6F44403Bo8d0PXLadT8u971rpBylnNeLRjXW2+9kJ1hPNNQ0pCbe8iHlOgpsFoqSuSw76m+AEm6sj9l1siwkX9IdSuRwrYUIEdrm0QJ+97xjneEPEeT/5VblhTrmDFyoJqk9RpnVGuHB+Xr4uV1bdKf9GVE+zIVouw6Jx53nqRP6sUkdBH+uq94EqIsl3OoU4wnpXJUa937OZ/Xq36RwQdOiIJP8h/RmORTBIr05IUrAIVfEqKVOBFXnBSE8XmAEchdP6fVSkbgYsAS2ymbcU8vpCyvYpRePOW82EfGis1XydZhc8xTE8D27srWpYZP2ugDkADhWlQwh0Toh4RU05uwcT91GZVmdn+jYFQyQZCrlsefBZjNAafpclotGBmtORtvkAoQBvCiDOCc8/VFEKqhD2LkEGAp9AUWH6YPOiXonfrMQOXD5iG7rgSJZz/72RUzLFauZU8Cbq6t2vYMPgb3SxnHHr1OLRhHO6T87UswJCUTxMtS16WlU2DSOGP6HRbSwCTXbrzxxoFHsXJtzjVy+voQciVsAWMOhQfquyqCcRJSFTBOQrWezzEEaMFwM/f6sBnrHo/2mpVkJBGpft59TqsFo0HunM0YqSCnmn5sRnGqnPP1FT7iyYm15Yr3nBdein0BBQhTMq/ZgJwNMwpzaIxHavOsv/76gUeqQ+ScH3lkJQXP0MYjdj+bVFGqnFYLRqEWxrQ5EykbG9G4qiKja621VqicmnJe7CP84G+p8WzPacMbOQRYbn05I6SoiEcujxRaEO3AIzHISP+U38gjUx3kQrbxqNfQjocVhyLhlONN2XjQJKNNwDXlHH3cQ38xKXFGnuW8xRlzPghj0Sbv+/ABalY8wtfNN988TF/omuIKjL1N4qdqRfGNjgjbDLm5h5K/RmDmtcA8aUcNUqVUdlsDBCsgWJDSVNVZ8cjcF6E7FUO6zAlgtMiRXMucVqumS03vHBJO3zeWw7OqQZfRD4wYrYi8qg1t6nL6J1u4gnuwFZlvBji6wEizmexFpee0AsYcag3UNye0sxzAyLkBSCM6Oa2AMYdaA/Vd1cCITACZK7ULGAcCWM5lOW2pFSWWg2T07oYXcx3RAsYc1AzUV84hZ0T+4apgMwIiO1ihqZxWwJhDrYH6Ume8aDZWl2pbDpLRwIUZi/Ijc1pvYEREowgycHImFTlv3ifx5zBsGjCitTil0ZucYUfn5XjTQjsXXnhhWCUhp2UawQAACz1JREFU592mBiND1c2lDJkYxPXPmftQwPiUfZUy7WASMEYeERSKP5n8JaaZ2iYB46KUN/GgxpXV85ZJLKu4lFFOZfNCP8NrpgKoiwOQbW0SMOKRmKRCAUa5dtxxx1DxrO0+o8eWDRjNKFNJ1VipgXiTygsYR1nZ/XfOVNVJwGiyFolIWuGVoVvl91JbLhglUogQfOpTn0q9Reg3tZpmdPOcxMoUK7eATQFjFg8C7cwFSpnEPwkY8chwo8lu5lVbsmNIMDILYiZSDiWmBqMbx5sbJy01vXPIv9CX/WaCWkp5k0nAOMojM/+UUR4SjPkUWDhjajDGG7N1ChgjNfJ+SS2JIpIQuubATALG+DR4JPZXwBgpMvbLHpn30I5JUQCp0FLXeO5yACOecsYk2Oa0IhlzqDVQX2oUA7syqN1+OYCRvWjlLZ57TitgzKHWEui7HMAYk2sXrYxysRknRyqJOIvhwFnZjEsCjOJlVvtUrSC1FZuxClUfLIN22WWXda7jN61kFH4zZ0nya2rDo5zhQKBXa/yggw5KvUXo15ua9nWb3WfWmQpWqa2AsQqVFwyjGjDoWpRoGjDikdEy9pxFR1NbLhj1h4VFy9qJsUYjMoa3UlsBYxXGiY1gpawdOA0Yp+FRjmSMDhnTI6f1JhndND5ETt2WAsYFMA4Z9B4FxKQ8ygHj6P1y/u4VjDk3jn0LGKuwioDVBCyjRvK1tWkkY9t1247hUQ4YowQWP81pBYw51BqoL4OfeQNoXan6ywGMbFPDjRdddFEWxQoYs8g1TGdmDQYCIqnS1pYDGNmKvZVRLvOm2+CwuMeWAxh7jTNuuOGGlbgXhPtih9zcw6RwVVvVlZ7Hmt5sMnTInQOjysOseKSYqwQLIaiuSfzAqIzyNttsk/Xl1qpppXZdTBDbfIkhN/eQ5Wz943ktMB+nA1ijL3V2oKUxFPycFY8seKSujxTBLjCygc10BNycVgtGZdPUSVFbReWqrk0/M8EsjGMDqq5z4nHnkoi+In9LQ+sy4nNecDn0zZk3bUKVsiHqp++www4z4xGebrXVVtVRRx0VsqzaeMQGNuGLNM1ptWC0IqahKROrUjarKKn/onLZ6quvHirop5wX+7iXkRs1p6WTUVvz1HIqSigSZfTEcFsuj4477rhqjTXWCDw64YQTkng7zqN77rmnsyTepLyrBSM7JGcTT6LK99lnn2qDDTYIw1o558e+Kd7kpC+6lM/LAWMMWlOFkW4pv3gESBtttFHg0c0335x1frzHkDyqBSMxm7NZv8Q8mFhg3lowOefHvl1hjaUMqGmezfIYtIJk1JT5zOgUaZb6i0cWIVJKzyIAlnRLPXe0XwqP9HE/nn9OqwVjzgX09dWU1Q5yqfZUf94nEHY5Bk+dkf8XHs2qpjfpyYzIXfWiFoy5oRx2jIWxo5pWxy/3GvqzFVO+vHxWrDpnRKmYS188sjARyciUuuWWWwbjUa9xRuGCnM3stlhg/pnPfGYooZxzvr7zXGA+51MBQk7e448/ns2ja665JgARjy6//PKs8yOPlK7xDG1Co1cwqhUt3KLWtnBL16bes3Pi6ktqP3edE4+7h7CQa5gdh8hedp6a2KIAtoRXtlZbM4b94Q9/ONArl0fWDRRDtkLWlltuORGPzjzzzDCO3sYjYOytjPJqq60WSuaqHa2Yecrm5vor+JN7ngUXBVQtnmmJL57iPDUfoLDLG9/4xiD12t6dVERfqlaWTy6tJ+WR7P1tt902FGlQoaKNR2xGy/exG3Narc1IwokvCQcYohpy86VLTzrllFPmdjgwJ7QTx6Zpn/vvv39mPBK6U4kiZQQGAElOEjKn1YJRogRUQz+nYsjNPXxpp512WgHjvvt2lhOMYFRg3hDdrHgkWpI6Ng2A0dHqBYxXXHHFTEZCAH3eJ/GbwG9cWill4Z22NgrGpbragefH1zZVXveOjZKxgLGOXMPsoxkAS1C6Kzt6OYBRkNx4u1BSTitgzKHWQH2jFGFjYWRbWw5gJBEXtaJEGwHbjhU13UadHz62HMDoo+otn3HSTG/A4kX5TW0FjE/ZV7OQjJPyKGdClvfobe3AScBIvQjeSpQVrU9tBYxVKPp+9913V5/85Cc7wyHTSEY84hWrEJaSkBF5iEe5YDQZS1ntnNaLzSgOKWtHjpyVUgXJU1sBYxXK4VmbWdXfobxpPOIgqY6rcgVAprZcMOoP9JyynDY1GIlkq6IiptoqyqCdfvrpyc9QwFgNXkZZksTtt98ehlvxCY9k8KS2XDCKMXJiDGjktKnBSDVbjNsIipw8uYylpncOC4avKEG1n3322ZUMftk6tNcqWUbZFyA29v3vfz9UXpXsUMCYB0Y2NhNHBbchyiiP8ujBBx+sDjzwwMHBSJq6b06bWjISyW7MJhHoLAXmc8i/0NfHLIXOGDU6trVJHJhRHs2iwLyIyqc//emQxNH2LuPHpgZjvKCvoBSYj9TI+41gwUR/t7VJwBivh0ezKDAvq3xRK0oUMEaWD/u7HMAY44yljPKwWBjk6iQiaUJFM3naWgFjG3X+/1iRjAlEaujC+ZM/ajy3q9DqcgAjLFx77bUhlNTwyrW7i81YS5bZ7mRrH3nkkaFyrWmrbW05gJF0FxWQtZ/TChhzqDVQX6NXgtE77bRTKAnS5sQsBzAi06KEdiJ/4tdgJU3p8KnNefOeXGsIUBU25WG+9rWvtdqN04ARrZ944okwGpObP5AzNu1javugmrDRm2R0c7YCm6crVjb6MAWMVaDZbbfdVp188smhTAyHpqlNA8ZpeJQDRh8XO7irotr4O/YGxvELp/5fwFiFhFreNOb5oNukyjRgTOXJeD88ygEjZ8xoksSMnFbAmEOtgfoCn/QuUzyXc6a3ZycVLVVsWNhoT04rYMyh1gz6koxyDQWO6yTkUpaMnlnSDEdMDcle6jNOklw7KZ+Kml6ZcvIMZUkbtqtT2UsZjD4iBRkOO+ywkMvI9MhpRTLmUGsGfSUY7LXXXtWhhx4aimkB5GhbymD0rGrxSJgx47FOso++y/jftWBUYF4lWV4xdA+5uYdA76mnnjq3k/hHmSJYfNVVV4USydLKZPPQHrFFMG6xxRaVdLBZ8UjdccnT4wXmAc7zRbsXVtQLGv+I4vO3/daCUWGgN73pTdUNN9xQ3XTTTYNu7mGOtlR4hYzmsdbOKIOEdQTBzz333JCRTVKOhnrEZNU12mSTTarzzjtvZjxStWz33XcPKYKkHvsQ6MQtFa2S1Z0rCUff29+1YFRrRy2XrbfeOhR+V/x9qM09VMRSrkPlW8FYXuU8N+/PK5WNTVKOSkYF5lesWFHJiFkMHh1zzDGhIq3nExvlNZtXY+ng0Y9mEv7VglENF5NpuOYM6SE394ibNWB8bV3hjUledDmdQ8IApAGEUSdGYXkJCOavkJhK6H3xi198kj/oqPqXfTY89H/kY6Sz/W19nBP7+B29Dh6xCY2lW9mCfWsqA1txWr7VglHm8aw3Yp7944WmFffLCXipz4oubEl2m1qWMupJSNXBIq+s8cysuuSSS6p3v/vdlVUo7r333iBd9RFU1199R8dtVkwwBEni8oaZAYZznSuLyHb99deHoLc+PhCq2WiR8oc+CCEck76m5VstGFMJVPrNjgLAaBbm1VdfHdZiIZUs5KRoVGxKWR9++OFBfVvVgPmjriKAaaTto48+Gmw/x23MpDvvvPNJCUwzATMzgF1q8aNXvOIVAYCcE4Ajrd0X+KMAic8wzW8B4zTUK+f2SoECxl7JWS42DQUKGKehXjm3VwoUMPZKznKxaShQwDgN9cq5vVKggLFXcpaLTUOB/wP3/WYuEkEZpQAAAABJRU5ErkJggg==[/img][br][list][*][math]x[/math][/*][/list]
[list][*][math]9[/math][/*][/list]
[list][*][math]3[/math] [br][/*][/list]
[list][*][math]x+2[/math][/*][/list] [br][*][/*]
[list][*][math]3\left(x+2\right)[/math][br][/*][/list]
[list][*]the equation sign[/*][/list]
Select the word from the following list that best describes each situation.
You deposit money in a savings account, and every year the amount of money in the account increases by 2.5%.
For every car sold, a car salesman is paid 6% of the car’s price.
Someone who eats at a restaurant pays an extra 20% of the food price. This extra money is kept by the person who served the food.
An antique furniture store pays $200 for a chair, adds 50% of that amount, and sells the chair for $300.
The normal price of a mattress is $600, but it is on sale for 10% off.
For any item you purchase in Texas, you pay an additional 6.25% of the item's price to the state government.
[size=150]Clare drew this diagram to match the equation [math]2x+16=50[/math], but she got the wrong solution as a result of using this diagram.[/size][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdkAAABrCAYAAAA7MvjIAAAVFklEQVR4Ae2dCbCN5R/HZSfkZklUQoUQibL11yR7NZaKRlqUYio0o2RaqEkpwqCiCBVKiUQp0jaJmJEtW3bZk12W+v3n+zTnOvc69973LO+5597zeWbeOe9532c7n+d53+95tt+Tx3AQgAAEIAABCPhCII8vsRIpBCAAAQhAAAKGyFIJIAABCEAAAj4RQGR9Aku0EIAABCAAAUSWOgABCEAAAhDwiQAi6xNYooUABCAAAQggstQBCEAAAhCAgE8EEFmfwBItBCAAAQhAAJGlDkAgmwksW7bMlixZkuGxa9euDHN4+PBhmzt3ro0ZM8YmTJhgiuvMmTMZ+ucGBCAQXwKIbHx5kxoEziFQpUoVS0lJyfAYOXLkOWF0YebMmVazZk0rWrSo5cmTx/LmzWsXXnihderUyfbv3x8yDBchAIH4EkBk48ub1CCQhsCff/5pJUuWtDJlyljHjh2tQ4cO5xwS0/Ru8eLFVrZsWStRooT16dPHvv32W5s+fbq1bdvWChQoYDfddJP9888/6YPxHQIQiDMBRDbOwEkOAsEENm7caMWLF7emTZsGX870/N9//7UWLVq4lqu6iNM7iXW+fPls3Lhx6W/xHQIQiDMBRDbOwEkOAsEEFixYYEWKFLF27doFX870fMeOHa5ruUGDBqYx2fTul19+ca3ZqlWr2vHjx9Pf5jsEIBBHAohsHGGTFATSE5g9e7YVLlzYunXrlv5Wht/nzZvnWrH9+vUL6efEiROu+1nxbtmyJaQfLkIAAvEhgMjGhzOpQCAkgUmTJlnBggVtwIABIe+nv6hx1oEDB7qJTmPHjk1/231Xd3Lr1q2dn59++imkHy5CAALxIYDIxoczqUAgJIFBgwa5VmnPnj1tyJAh9sgjj9hjjz1mb7zxhi1atMhOnz6dJpy+a/awZhN/+eWXae4FvkhkH3roIecn1JhtwB+fEICA/wQQWf8ZkwIEMiQwfPhw15LVjOBixYq5JTj61MSl/Pnzm8Zd9+zZkxr+1KlTdssttzgBVbdxKCeRlVBLiCXWOAhAIPsIILLZx56UIeAMR2iikmYZHzt2zE1U0qeW7dSpU8cJZf369U1LfeROnjxpdevWzVRk5W/o0KGILPULAglAAJFNgEIgCxAIRUAGJWrUqOHEcuLEic6Luou1llat1Mxast27d3d+Ro8eHSpqrkEAAnEigMjGCTTJQCBcAur2nTZtmhuzVfevvstkosZvJbJTpkwJGaX8denSxfmZMWNGSD9chAAE4kMAkY0PZ1KBQEQE1JVcqFAh69y5s5sEJQHVjGSJ7IgRI0LGKT+BLuVVq1aF9MNFCEAgPgQQ2fhwJhUIRERAxv9lk7hv376p4SWcMmDRtWvXkKYTZaxC9oxlxzizzQVSI+QEAhDwjQAi6xtaIoZAdAT+/vtva9asmWu1fvTRR6mRaVy2UqVKznbx1q1bU68HTiZPnmznnXeeNWzYkB15AlD4hEA2EUBkswk8yUJABJ5//nmTwYgDBw6kAbJu3Trr0aOHE9gbb7zxnPva2k5LfGR0YvPmzS6suok1GapChQpuOdBvv/2WJk6+QAAC8SeAyMafOSlCIJWAWqRaF1utWjXX8pRx/0aNGln58uVdN7EEdv369an+AyeySfzoo486oa1YsaK1atXKbTJQqlQpF5+sQuEgAIHsJ4DIZn8ZkIMkJvD999+72cIS0+rVq1vlypXd+tj27du7TdgPHTqUIR0JrSw6qUtZ4bS3rJb3fPXVVyHHajOMiBsQgIBvBBBZ39ASMQS8E9DSHBn2l3DK4IS6fr062TNWOI3hhhPOa/z4gwAEIieAyEbOjpAQgAAEIACBTAkgspni4SYEIAABCEAgcgKIbOTsCAkBCEAAAhDIlAAimykebkIAAhCAAAQiJ4DIRs6OkBCAAAQgAIFMCSCymeLhJgQSh8DRo0dt9+7diZMhcgIBCGRJAJHNEhEeIJAYBN566y1r2bJlYmSGXEAAAp4IILKeMOEJAtlLQJu2V61a1VlzWrt2bfZmhtQhAAHPBBBZz6jwCIHsIzBo0CDLly+fM/zfuHFjO3bsWPZlhpQhAAHPBBBZz6jwCIHsITB//nwrWbKk2yxAu+toL9kXXnjB7S+bPTkiVQhAwCsBRNYrKfxBIBsIaKJTuXLlnLDWqlXL+vTp4861x+zUqVOzIUckCQEIhEMAkQ2HFn4hEEcCK1eutGuvvdaJqravW716tR0+fNiaNGnirmlT9o8//hh7xXEsE5KCQLgEENlwieEfAj4T0AYB48ePd/vCqmv4ggsusFmzZqWK6b59+6xGjRpOaLVNXu/evW3//v0+54roIQCBSAggspFQIwwEfCKwY8cO69atm9snVuOvV1xxhc2ZM8e0S0+w04bst956a+pkqHr16tmiRYvY4i4YEucQSAACiGwCFAJZSG4C2qpOLdHp06ebNnGXuObPn99atGhhBw8ezBCOtrZ7+eWXrUiRIq5VW7RoURs8eLBt377dTp06lWE4bkAAAvEjgMjGjzUpQSANAXULL1261Jo3b+7WvwZmDhcsWNB1F58+fTqN/1BftH+sxm7VbayuZcVRuHBhu/LKK23y5Ml25MiR1G7mUOG5BgEI+EsAkfWXL7FDwG3CrnHULVu22JIlS+zdd9+1nj17WuXKlV2LNSCOZcuWtfbt29vy5cvDFkYZq3jiiSesSpUqrgtZceq46KKLrE2bNjZq1ChbuHChbdiwwXbt2sU6W+olBOJEwDeR1T9sPcwrVqywb775xsaNG2f9+/e3zp07u4deDz4HDHJ7HWjdurXJeISsNZUpU8a1NAMCqM9SpUrZbbfdZmPHjrXff/896jHVvXv32syZM6179+5OxGXAIji94sWL2+WXX27XX3+9tWrVimeQ91DS1IEOHTpY3759bfjw4W6eg3qRNm/eHPUzl5VWx1xkNbY0b948909dL5bAIvrgB53z/1oZcEguDpolXLFiRatTp44bbx02bJhrtWpM1g+3bds2t5a2U6dOTlTVypWopxde6mFy1UPK+7/y1hwGPY8S3w8++MD1NPnxLMZEZE+cOOG6ofr16+cmbmjShgpS40OalJGSkmKXXHKJ1a9f3x588EEbOXKkvffeexwwSIo6MGnSJFu8eLFt2rTJ1G2s5yXeTrOTDxw4YFu3bnXrbbW+lmeQd1Cy1IEJEyZYr169rGnTpnbZZZe5XiXNYwj+w6meJvW0/vDDD3bo0KGYPaJRi+z69etNlmg0WSMwcaNAgQKue0xr/fRS0QJ6zXZUF7IOHAQgAAEIQCCeBAL6owmF2jZS8xi07O1///ufFSpUKHVYRcKr+RH6IxqLlm3EIqvENZlC3U9qtUpk1R01cOBAW7NmTbb8W49ngZEWBCAAAQjkfALSMi17U2tXgqt5C9I09ch27do1akMvEYmsZijeeeedqTMjZfpt9uzZdvz48ZxPnF8AAQhAAAJJSUCCq6Gdjh07pnYl161b103ejRRI2CK7YMECtwZPSq9u4fvvv99kpQYHAQhAAAIQyA0E1GBUT23p0qVdq1Z2wmX4JZLhzrBEdtmyZW4CkwRW3cQaNMeyTG6oUvwGCEAAAhBIT0CaV7t27dQhUXUphyu0nkVWg8Q1a9Z0iWlQeM+ePWEnlv4H8B0CEIAABCCQyAQ0cVdr2QPjtD/++GNY2fUksuqnViKaPax1r+EmElaO8AwBCEAAAhBIIAI7d+5069sltNp2UvOSvDpPIvvKK6+kDgJrQHjatGluerOmOCfqIQs66lOXCbtEzSP5Stz6Q9mcLZsxY8a4Z0kL9uFylgsskovFiy++mLpMtV27dl411jyJrNSbAwbUAeoAdYA6QB34rw54VdmwRFZm4cqVK+eMjsvweKIeymNgcbEsTuWEPCcqS/KVuPU8HmWjZ0erCPRi1frBeKRJGsld5xK5/PU85M2b1z0PvoisjPwfO3Ys4Q9Nv27WrJkD0aVLF2cYIyfkmzwmft1KtjLSnrXaTEDzMbSEIdl+P7+XZzK4Dmg1jZbz6E+nV+fJZ6B74P333/cab7b704bXyve9996b7XkhAxDIyQQaNGjgRHbo0KE5+WeQdwhETUDLdwJWDr1Ghsh6JYU/CCQpAUQ2SQuen30OAUQ2CAkt2SAYnEIgCgKIbBTwCJqrCCCyQcWJyAbB4BQCURBAZKOAR9BcRQCRDSpORDYIBqcQiIIAIhsFPILmKgKIbFBxIrJBMDiFQBQEENko4BE0VxFAZIOKE5ENgsEpBKIggMhGAY+guYoAIhtUnIhsEAxOIRAFAUQ2CngRBN27d69pQxa90L06reXcuHGjrVixwn799VdnWzec8F7TSXZ/OUZkDx06ZJ9//rn169fPZANSBiNGjx7tdqfXZgSxcIhsLCgSBwTMENn41AIZOpB96KpVq7r34okTJ7JM+OjRo/bOO+9Yo0aNLCUlJdUakazzySgPLrYEcoTIyqj2pZde6jYckHkqWZIJHCVKlHCGyGOBBZGNBUXigAAiG486IEHt3r27exfKiE79+vWdda3M0lbrtWnTpk5YCxcubD169HCNlTfffNOeeuopO3nyZGbBuRcBgYQX2TVr1jhrGbKBql1y1q5da7t377bNmzfbpEmTnG1U3VuwYEEEPz9tEEQ2LY9E+bZq1SqrV6+e3XHHHZa+1+L06dPWqVMn94L58MMPEyXLSZ8PWrL+VoHVq1c705UFCxa0u+++220nmpXI6tnRO04Nlccff9zt733mzBnXxSwhSP9s+fsLkif2hBdZFcVnn31mf/zxR8hS6d+/vzOFeN9994W8H85FRDYcWvHze+TIEatbt67lz5/f9Kcr4PSCePLJJ931Bx54IMt/8YFwfPpPAJH1j/H27dutevXqpl684cOH219//WVlypTJtCWrF/2MGTNMonzXXXeZ7Evj4kMgR4hsZig0cK+ukoYNG2bmzdM9RNYTpmzxNHPmTDdcoDF5Of3rnjJlits56eabbzZN/MAlDgFE1t+yeOmll2zOnDkuEU14ykpkJao1a9Z0Irtw4UJ/M0fsaQjkeJHdsmWLE9mWLVum+WGRfEFkI6EWnzCa+BbYfnDbtm22aNEi00SN8uXL286dO+OTCVLxTACR9Ywqao9eRFbPTL58+Vxj5ODBg1GnSQTeCeR4kdWAvVqyffr08f6rM/CJyGYAJkEuv/rqq248aeDAgVarVi0rVqyYbdq0KUFyRzaCCSCywTT8PfciskuXLnUTpB5++GGXGfUAPvvss26VxtNPP+2W8Piby+SNPUeLrCa9XH311W7Q/+eff466FBHZqBH6GoG6vC6++GK3IXjJkiXt66+/DmtdoK+ZI/I0BBDZNDh8/eJFZNW1rMbIgAED3Ixk/UE9//zzrWjRoqZZxoUKFbI2bdqwhMeHksqxIiuB1T8wdYH06tUrJmgQ2Zhg9C0Slble3npZaKITLnEJILLxK5usRFYveU2Q0nNTsWJFq127tn3yySfOxsCOHTvc0Ev79u1dL9Htt9/OLOMYF12OFFm9bCdOnOhaNI0bN7b9+/fHBAsiGxOMvkSiMte/cM0w1gzJ6667jtnEvpCOTaSIbGw4eoklHJG97LLLbOXKledEq4mDMmihFm6s3qfnJJKkF3KcyGrZxoQJE1wXhybC7NmzJ2ZFh8jGDGVMI9JM4qlTpzpx7dixo2lcSWL7xRdfxDQdIosdAUQ2diyzismLyA4bNsy1ZJ955pkMo9NySPUM6v2Kix2BHCey48ePd+MHZcuWNXV1xNIhsrGkGbu4vvvuu9Q/VQcOHLDly5e7f9x16tQx/enCJR4BRDZ+ZZKVyCons2bNciL72muvZZixIUOGuC7jkSNHZuiHG+ETyFEi+/bbb7uX61VXXWXr1q0L/9dmEQKRzQJQNtyW8YlKlSq55Trr1693OVDXcefOnd1wwYYNG7IhVySZFQFENitCsbvvRWS1CYAsPQVmF4dK/bnnnnMt2VGjRoW6zbUICeQIkVUmZTJP4wUyaq21sX44RNYPqpHHuW/fPmvSpImbBSlrNaoHATd//nz3QlCZSXRxiUUAkY1feXgRWfUAaUa+1pWHWvamHqFmzZq5XkKtqcXFjkDCi6zG4zT9XFPN9eD6JbBCisjGrmJFG5MqpkwmVqlSxUKNIx0+fNiVl3o1/KwT0f6OZA2PyMav5L2IrN6jaqFqzPWee+5JY8BFO+9o9rGW8ch8KUMwsS27hBfZuXPnuhasKoe2tlOLNtShiTHaPCAah8hGQ4+wEDhLAJE9y8LvMy8iqzxoh50OHTo4odVMYk10Gjx4sFsfK4HVTmfLli3zO7tJF3/Ci2zv3r3dgL3WeGlMIaNDW9+9/vrraboUwy1NRDZcYviHQGgCiGxoLn5cDYisdqrSVnaZObVaR4wY4RoueqcGtgzVHAfmN2RGLvJ7CS+yGrDXeFxWx6effhp1JUFkI69IhIRAMAFENpiGv+d6iWsjdq8brqvrWPaLNalQM/V37dpl2vwd5w+BhBdZf3526FgR2dBcuAqBcAkgsuESw39uJYDIBpUsIhsEg1MIREEAkY0CHkFzFQFENqg4EdkgGJxCIAoCiGwU8AiaqwggskHFicgGweAUAlEQQGSjgEfQXEUAkQ0qTkQ2CAanEIiCACIbBTyC5ioCiGxQcSKyQTA4hUAUBBDZKOARNFcRQGSDihORDYLBKQSiIIDIRgGPoLmKgO8iq31ftQYrJxzNmzd3hi+6du3q7OHmhDyTx5xRt5KpnGRL+oYbbnCGDrTrSzL9dn4rz2P6OqDnoVSpUk5bvP57yOPFo6yJ6Ljmmmuc2a7WrVtboh+lS5d2ea5QoUKOyXOiMyV/iV/vY11Gbdq0sZSUFPcsVatWLeGf+1j/fuJLvjqfWZm3bdvW7RgmPfTqPPkMiCyf//3ZgAMcqAPUAepActeBmIqs18jwBwEIQAACEIDAWQKeWrJnvXMGAQhAAAIQgIBXAoisV1L4gwAEIAABCIRJAJENExjeIQABCEAAAl4JILJeSeEPAhCAAAQgECYBRDZMYHiHAAQgAAEIeCWAyHolhT8IQAACEIBAmAQQ2TCB4R0CEIAABCDglQAi65UU/iAAAQhAAAJhEkBkwwSGdwhAAAIQgIBXAoisV1L4gwAEIAABCIRJAJENExjeIQABCEAAAl4JILJeSeEPAhCAAAQgECaB/wNcYlahjuFTKQAAAABJRU5ErkJggg==[/img][br][br]What value for [math]x[/math] can be found using the diagram?
Show how to fix Clare’s diagram to correctly match the equation.
Use the new diagram to find a correct value for [math]x[/math].
Explain the mistake Clare made when she drew her diagram.