IM 8.4.3 Practice: Balanced Moves

[size=150]In this hanger, the weight of the triangle is [math]x[/math] and the weight of the square is [math]y[/math].[/size][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMUAAAEzCAYAAACBhMdAAAAgAElEQVR4Ae1dCXhURbaepyTpfe9OZ9/3fSeBLES2kBAIBAggLjOjKKO4DOIGIqIwMgKyKS6jgOyghlGQGQXFHVzGBUfFGRh3nXHU2fQt897/vlNJYyd0knu7b98k9LnfV1/fvl23qu5/6u+qOvfUOT8CH4wAI9AFgR91+cZfGAFGAEwK7gSMQDcEmBTdAOmPr//3f/+Hf//73/j+++/xz3/+U3zSd7rOh/oIMCnUx/y0GokAX375JTZv3ow1a9Zg06ZN+OKLLwRRTsvMF4KOAJMi6BD3XcF//dd/4fXXX0dOTg4iIiKQnZ2NV199FXSdD/URYFKoj/lpNVLnf+2115Ceno4f/ehHSEtLw9GjR5kUpyGlzgUmhTo491oLkYJGBg8pUlNTmRS9IhbcH5kUwcVXUulMCkkwqZaJSaEa1D1XxKToGZv++IVJ0R+od6uTSdENkH7+yqToZwFQ9UyKASAEryYwKbzA6K9TJkV/Ie+7XiaFb1xUvcqkUBXuPitjUvQJUfAzMCmCj7GcGpgUctAKUl4mRZCA9bNYJoWfwCl5G5NCSTQDL4tJETiGAZfApAgYQkULYFIoCqd/hTEp/MMtWHcxKYKFrIxymRQywFIhK5NCBZD7qoJJ0RdC6v7OpFAXb5+1MSl8wtJvF5kU/Qb9DxUzKX7AYiCcMSkGgBSYFANACF5NYFJ4gdFfp0yK/kLed71MCt+4qHqVSaEq3H1WxqToE6LgZ2BSBB9jOTUwKeSgFaS8TIogAetnsUwKP4FT8jYmhZJoBl4WkyJwDAMugUkRMISKFsCkUBRO/wpjUviHW7DuYlIEC1kZ5TIpZIClQlYmhQog91UFk6IvhNT9fcCQgjxsh2r6z//8T+EhkNxlkttMj4dAuh6qmPSnx/UBQQoC4H/+53/w3//93yGZ/vWvf+HIkSOCDESKlJQUvPTSS8Itf6hiQv2hv4jR76SgB6eYDLt378aWLVtCMm3cuBG33nor3G63GCkiIyOxZMkS0PVQxYT6wz/+8Y9+IcaAIMWHH36IuLg46PV66HS6kEtarVa44D/77LMFKeiTXPLT9VDEg/pBTEwMTpw4gf/93/9Vd0EB9H94L3roP/3pT3A6nTjrrLNAHUKj0cBgMIRkog4Rqs9Ocif5Uz9wOBz4wx/+wKQgQFwuF1pbW3H11Vfjqquu4hRCGEydOlVMIakfMCk6R4ohQ4YgLy9PrC8+++wzcAotDB555BEUFhYiLCyMSeGZPoWHh6O4uBhPPfWU6vNIrrD/EXjmmWdQXl4O6gc8UnSOFEyK/u+Y/dkCJkUn+t4LbSZFf3bJ/q+bScGk6P9eOMBawKRgUgywLtn/zWFSMCn6vxcOsBYwKbxIcfLkSaFtIFVcUVERa58GWGdVqzndSfHBBx+E5ss7Mnh76623YLfbMCRsCLKzs/HYY4/h3//+d7/YvajVAbieHxAg+zdSuPzmN79BQUGBeE9hs9mE5TCZ1at99KvtE4Hx1Vdf4ZprroHOoEW4fgj0Rj2uv/56/OUvfxHEUBsQrk99BIgQf/3rX7Fo0SKYzCZEGIdAa9BizpxL8eWXX6r+59hvpCBC0Cjx+OOPIy0jDZZYLbIm6mFJiEBRSZG4TibVfJz5CHz33Xd48sknMbSqAqaYcGRPMsCaqEVicgJ27dolosdSf1Hr6DdS0L/DJ598gpkzZ0Jv1iKn1Yjx6y3InaqHLdqIWbNmgaxn+TjzEfj0008xe/Zs2KMtyGrRi36QP9MInVmDSZMmCWtZmk6rdfQbKf7+97/j/l/dj9T0VDgyNGhaZ8G0nQ6MvcOC2DIDYuJi8NCWh/D999/3y2JLLQGEcj3070+7Cx955GEkJiUiukiPUcssaNtpw4QNVrhyNUhMScDatWvxzTffqAZVv5CCwHjttdcwvnk8LG4Dyi4xYfpuO2a2O9G2y4HSi4wwuiIwctRIMVrQLiw+zjwE6N+fjD6bmptgcESg8Hwjpu2wiX5A/aHyKhOs0QaMHjMaL7/8svhzVGMapTopaNr0t7/9DbfffjvsDhsSawyY9IANMx9x4Ny9Tpzb7kTz3VbEVepgdZrF4otGCzXAOPO63cB9Is8occcdd8DusiKmVIumtVYhf+oHMx+1Y/JGG1JHGWCxWXDLLbfg66+/VkX5ojopaLh88cUXUVdfB70rDLU3mDF9TwcZBCn2OsWoUXOdGeYYDVJSU/DKK6+IxdbAFTG3TC4CpGR5551jyMnNgcmtQeUVZrTt7Pxj7PxznPGwAyNutsAYE46hVUPx9NNPi+m03Lrk5ledFF988QXmz58Pe5QVaY06TLz/h38HDyloGjVliw3Jo7QwWgyYfclsMczKfTjOP3ARIFXr1T+/GiarEQk1WrRutmPmo86O2QKRopMYNIvIbNHDFmXG5Zdfrko/UI0UNFzSi5gDBw4gMysT7hw96hd3rCU8ZPD+pOnU6F+YYU/WIj0zHdu2bRMqXJ5GDdyOLqVlJD9aI9KGopy8HFjjtKhfbPlh+uwhROfn9D12jFpqQXShHimpydi7d2/QVbSqkYIWVfTvcN7550Fv1SB3mgFTt3Usrr3JcOq83SkWXUUXmKAzadDW1qa6ak6KkDmPPASoH5Aq/oILLoDBrENem1H0A1pLnpK9FzFo1kCL74JzDdDbI9A6pRWkwg2milYVUngWVZs2bUJMfDTcBVqMWW4RiylfQHiu0Wgx4R4b3PkaJKcl4e677xaLdHli4NwDCQFSxZPrnszsDDizNBi/zkvJ4kUGTx+gTyJGw0orokt0cMe4hIo2mMoXVUhBw+Uf//hHlJWXwejSoOSiDtWb94P3dE4q2sorzbC49Rg1epRYdJMGi6dRA6mr990WkhfJ7Y033kBzc7NQxZdfauy6uO6BFNQ3aBFeOdcEY2QEcvNy8e6774ppWN81y8+hCim+/fZbLL5lMcxWE6KKdZj0oK3PUcJDEhotWu63InWMESazEcuXLxcvcghgPgYPAiQvGiXWrFkDi9WCpDq9mAWcUsX3QgjqC6SibX3IhtihWrE4v/a6a4W9VDAQCCop6N+B5n6HDh0S9kykehs+3wRStXk6fZ+f7U6hsq253ixUcxWVFXjuuedYRRuM3hDEMknJcvToUdSOqIXRHYbh88xC9d7TWsJXv5jxiAN1C0xCVZ+bn4t9+/aJ0ULpWUNQSUH/DqSCnTNnDix2EzIaDZiyteONpa+H7vFauxMtv7Iic4IeNrdZlEcvcvgYPAjQbIFU8Y5oK9IadJh4r+3Ui7oe5d599KBF93Y7sicbYbToxWL9448/VnzRHVRSkC/Q7du3g1htS45AwwprxyjRg6ahN3Dotf/I2yyIzNUjKTkR+/Y9LuxmlP6XGDzdbHC0lORDo8TBgweFNbQrS4/6RWZhztObvH3+1u4UqtvGNVZhL5eZk4kHH3xQceVL0EhBYBw7dgzk9Y1evBSeZ8C0HTKmTb7+JXbaQNaTBrsWjU2Nwi4qmKq5wdHtBnYrabZA9k1Tpk6BwaZFdqu+VxWsTzJ06wu06CZlDVlTjx8/Hq+//rqiRqNBIQUBQaPE3RvuhivShbgKvbBrkbqo6hGYdiea1lgRVaCFzWkVnro9MRwGdtcIzdZ5RgmycnW6HXBl68RsgVSsPcq4GwF85aN+NP4uG5JqDbA5bFi1ahVoekb9TokjKKQgu5a3334bI0ePhNY2BFVX/WAF6+sh5VzzqGg15nAUFRfhzbfeFG+6lQCDy1AWAVLFv/f+eyivKIfWFI7yOd3smyQQwGffEMoXO4ZfYxb2c8Nrhgura6W2rgaFFGQFu3jxYtjdViSP1Aqr15nt9oD+HTzgCNXcZruworW7bLjyqivFm3JlxcmlKYEAbTW+ccGNcEY64C7QCKtXkp9HloF80mgz8T6bsJ8j5cu8efOEql6JNaaipPAMly+88AKysjPhTNeh9kaTf4uqXv5FSKU78lYrbIk6FBQWoL29ne2ilOjFCpVB/YBGif3796O0rBTWOJ1QpcpSxfcifw+ZSPlSf7MZriyd2Kx28NBBRZQvipLCo4K96OKLoLdohQp16lY/VG99ANJhD+NA3nQj9CYtfvKTn/CiW6EOrUQxnsX1ZZddJqycSYXaq51bH/L2kOC0z3anKJcW73qrFtPapuGjjz4KeG2hGCk8owTZtcTExwj2knWjUsNlF0A8qrnVHXZR6VlpILsqemPKR/8jQEqWHTt2IDc/B45MDRru6LSCDXCB3aUPdBJJ2EXdQf1AB1eUS9jHBap8UYwUpBol+6b6+hHQmiNQ/GOTeNHi60GUukYvcsh+xhplQGNjo1ABK6WB6P+uNThbQPi/9957mNw6Wcil+CcGTN0agCpewihCVrS0iNeawzG8ejh+//vfB2QXpRgpPFtM3TGRcGZHoOVX9h5t5JUiBanmaIN78gijsKdZt36dUAUzMfqHUIQ7uSV64IEHYHfYEV/VoYpXei3Rvf8I5csmu7CidUU5sWDhgoDsogImBU2baJQ4fPgwqoZVwezWofpaE2hzSPfGK/693SnekA/7uRmmmAiUVZQJb4OkEuZDfQQIdxolaupqYIgMR8XlnZvIgjBt6t6XZjxsE4tuS7QWpWUlwtsg9Uvqn3KPgElB/w7kze/aa6+F1WFB2tjORVX3rYUShsHuDyr1ewup5hr0sLpMIkYerS38AUMueJy/KwK0lli4cCFskRYkj9SLUTzQF3VS+wBtZaXpdNZEA8w2I+bOnYvPP//cL7uogElBw+Wvf/1rlJaXwJoUgVG3Wfy2b5IKQPd8pJo7Z7EFjnQtEhLj8cSBJxRRzXUVOX/rDQF6cUazhbT0NLGFuPYGq+Kq+O5y7/K9U/lCm9cc6RHIL8wT3gWJqHKPgEhB/8YU6/jHP/6x8O6W12YQNu9dGhvEEeJUPZ1bFkk1Z7DoMGnyJJD1JI8WcruDf/kJZ7KGnnXeLIF/RrOuY3GtwrTpVB/o7Ge0qCc7O7KLapvehuPHj8vuBwGR4p///Cd27NiOuPg4xJTohXc/4a5GDSJ0q4MWW+NWWeDI0CIqNgrr168P+gZ3/7rQmXUXEYJe1JG1anxiHOzJGoz9ZZBU8d1k3p0Q9J0W9dQP4ofqERUTJdold7QIiBTEQvLyp7WGo+QnHWsJahRphdROVC+9IBp6mQUafbhQDZOVLgmMj+AhQPiSKn5c4zhoDREovtAEemHbn/2A1hbkdVJvD0P9OfV45513ZAEQECmWLVsmvLeRz8+6m8xo3mBF8z0WTOinRJ4FG1aYYUuNQKQ7EkuWLFHVB6ks5M+QzGSdSt4eo2Oihcd4mtOTHPqrD1C91A/JfVJUoQZmmwk33XSTLLQDIgUFWDEY9WJ/gy1JD2e6HylND0eqFtakcFgSw8SnPVXrf1kpOtEeo8mImpoa4VWO31vI6hOSMxOu5O1x9OjRIq4EuS6yJ+vhTPOjH6TrQXL37gfUL5xpOr/6gj1JD4NDI+KdJCUlSX4myhgQKaqrq0GJ3iJSqpaZPPeRl48ITTjOOvssGE0G5OXnobqGyvazzOF0X7UQFpl/kIaMF92y+kWfmQlPcjNDOysbGhrEH9Dw4R39wJ++QPLOL8gH/ZlRPwiPCBfGhJ4+IrcvdL2vus/n8c4QECnoXyLQRBa1ZOVqNpsxZMgQZGRkCL8+L730UkBl0/2UaL5L6kImhbfYlTmnl3WkfSSP4ErIi/x60eyD+oHJZMKePXtA/SPQPkb3yzkCIgW9MQw0kXkIGY/Z7Xbo9XpMnDhRvBUNtFy6n4Z3JoOc7iA/L+FLOCshL3obTvKnfkD9gfoF9Q8lypbzZAGRQk5FPeUlddnOnTtPkaKlpcUv3XJP5fP1wYEAkYu0mSR/DymoX8hVpyrxtEwKJVDkMgJGgEnhBSGPFF5ghPApk8JL+EwKLzBC+JRJ4SV8JoUXGCF8yqTwEj6TwguMED5lUngJn0nhBUYInzIpvITPpPACI4RPmRRewmdSeIERwqdMCi/hMym8wAjhUyaFl/CZFF5ghPApk8JL+EwKLzBC+JRJ4SV8JoUXGCF8yqTwEj6TwguMED5lUngJn0nhBUYInxIp3n//fUyYMEFYydpsNrGBiUzH1T7YSlZtxLk+nwgQKY4cOYKRI0dCq9XCbDFj5cqVoBgX9JuaB5NCTbS5Lp8I0CYlcoCw/JfLkZiUCIMjAjqzRkTCeuXVV8TOScqj1qEIKYjJ/iZycelrk5Fn15w/5aoFHtejDALkOv/5F57HmLFjYIszovA8M6KLtHDHuHDr0luFozWlQndJaXHApKBOSx2Y/P/Qnl256ZtvvhFzR5pD0o4rmlO+++67ssuheqkNtHWR2sTH4ECAZEXeHMkHbXxqrPBF3HyXDcPmmWFN0GLEyFo88cQTIvaIWnINmBTUGcmRLc0Hn3766c70DJ5+Wlp64sAB3Lx4MUwmMzQaLYYPr8aWrVtxSJQlrQxPvc8++yzefPNN4b1jcHSJ0G4ldXIaJR577DFUVFYgJt+M2hvMwlHypAdtSG/SISYlUsQ1/OCDD1QL4RYwKch15oEDBzBl6lSUVwztSEOHolxiKikrR2p6BsIiInD2kDDYHA7kFxZJvl/UI+qtQHVNjfA2Tf88fAx8BGhUJ1ldcsls2GOsyJ9uwcT7rcK7IHkYHHmbGVH5BhQU5WPX7p1i3UH3BPsIiBTEdFoT7NixE/mFxdC6YmHKKIYlu0JyMmeVw5RZBn16iUimzFLQNVllZJZCH58BsytKRDT6wx/+EGzcuPwAEaC+Q36jHnroIWTmZCC6SI/RS20gD/LkF1gEYnnIhsJZJthjjbjwpxeKSFV0T7CnUQGTgvTI27ZtQ3ZRKRyVzSi6dhMqluxVNZUt2o208xbBkpaPsWPHgoZaPgYuAtSpaR164uQJjBs3Ds4EM4ouMKJ1sx3e8SyIGOSsObZch+T0RNx7772qjBaKkSKnpByRddMw9LbHULPmBdSsflGdtOYFDFtxCNmXroA1s5hJMXC5cKplRAj6M12+/HZERjuRVG1C4+qOUeJcb/f9FP10qwPll5phT9RjbONYvP3220H3+KggKSrgrp+OymX7Ubv+iKpp+KrDyJmzCrasEibFqa43ME9olPAEeCkfWi5ibFddaUHbTofPSLrkvX78ehuSRugRGefAstuX4YsvvxCaxmBNo5gUA7PvnLGtolHi008/xeWXXw5nlB3pDQZMvMfWQQjvUcITi6LdKdYZFNfQkaZFcVkRfvvb3+K7774T6vdgAMWkCAaqXGaPCJC2cueunSgozIcr3YCRt1jFKOErAMupa+1OtNxvR2azEWaXARfNvggnT54UC/UeKwrgByZFAODxrfIQoOkOrQnOO28WnDE2FMw0YcoWm6TQ0qSiHbXMAnt6BNIyU7Bx00Z8/fXXQdFEMSnkyZVz+4kATZtIfb9u3TqkZ6UjvtyEpjUd7yS8NU6nRgfP9Knzk/JQhKLCWR3x7FomTcTvfve7oNhFMSn8FDLfJg8Bsnx4/fXXRTg4W4wBlVdYRCcntWtPROh+nRbdFKkoplSP2IRo3LHiDmFFS2UreTAplESTy/KJAE2bKHoqhYNLTItHykgDmu+yyw8tTYvuPXbQotsap8OYcaNx6NAh4ZlcSU0Uk8KnGPmiUghQZ6V/8oMHD4poV9E5Zgy/pnOU8KVt6jZtOm20aLcLU5CU0TrEpUXh+huuF4tuqkMpYjAplJI+l+MTAbJVolHiyquuFIvrnMkUKLQjemr3Di/1O5mCjLjJDHeuHqUVpdj7672ngrv4bITMi0wKmYBxdukI0D/3d99/hz0P70FuQY7oxOfcbEPbLt8v6qSSgtYhkzfakDfNAEecCXMuu1QEfCGLWyVGCyaFdBlzTpkIkMaJYg7SHhlnvAV5M4yYvNHRxb5JKhG656NF96jbzIgu0SAjNw2bN28W2i0lrGiZFDIFzdmlIUCEIKcUq9esRmR0JOLKTWhYaRVvp7vYN/WxhuhOhlPf253iHUfJT42wxunROH4cyDqa3nQHOlowKaTJmHPJRIB2QVLE1Oraapgjtaj4mQnTerBvOtXRZRKERoumtVbEVergjLbjztV34i9/+UvAuy+ZFDKFzdn7RoBGCVpcz792PqLjIpFcb8CEDfaON9d+aJx6JE2nXdTQy02wJupQWlGCQ08fCtguiknRt4w5h0wE/vWvf2Hv3r0oKy+FM82I+kVWTNvhkPySrkcS+BhJZpKK9j4b0hr0MDsNmHvlXHz00Ydim6vMZp/KzqQ4BQWfKIEAzecpHvbsS2YjMt6J3KkmtD4kzb5JDhm885Jd1Dm3WGBLikBBcZ6Ivx2IXRSTQomewGUIBGjaRFawDzzwAPIKchFXasKY262YvsepiMbJmwje52QXRZuR8toMQss149wZeOPNN/y2i2JScIdWDAF6q3zs2DG0trbCHmtCxaXWDitYGfZN3p1dzvkM2ox0lw0xJXokpiRg3fp1woqWFvxyDyaFXMQ4v08EaNpEUxZSwSalxiOp1oCmtXYxSiiigvWxnuhCmk67qKGXmWCJ1mLCpGa8+OKLYuSiEUzOwaSQgxbn9YkAEYJempEKtm5EHSLTzai8woip27o6IujSifvq5P783u7EhA1WJNXrEJ8Wg8W3LMYnn3wibK98NryHi0yKHoDhy9IRIELQKHHtddeK9wVZzWYxlaEFsCqjhBeB6F1I9XVmuDL1qKquwpNPPSk8gEh/GoBJIQctznsaAjRKkC+m/fv3o6C4AI50LeoWWH54UUfvJVRM9EKPHKplTTTAGWfB1ddcjQ8+OH5au3u7wKToDR3+rU8EaL5+4sQJTJs2DY5YC7InG8R+aholqIOS8Z7aSVjRLrLCna9FTkGWcLjW54N4ZWBSeIHBp/IQoFGC7JvuvvtuRMdEC99MpRcZcc4SK0bf3pFIJSs1ee7p/in1fsrnubf2RgsSa3Uw2fVoamqS9WBMCllwcWZvBGgt8dprr2HMmDEi0Eq4dgh0zjAY3eEwRvmbwmBwdySjO8z/ctzh0FjCMCT8bBiMBu9m93nOpOgTIs7QEwK0f4Fcpra0tKC6uhrDhg3DsOFVGFZNaZjMVIXi0iJERrkQrgmDRheB9Mx0kMM0+WVR3VWiLVXDqlBVVdXTI/i8rigpIkeQh8B9qF3/sooeAl9Gh4fAlewh0KeIg3eRXox99tlnwqyDXtqR+xp/01tvvYV9+/ahvr6+I7yX2YwVK1bg6NGjfpfp3RY5KChIinJEjmjD0KWPo3bdS6qlmjUvYfjKZ5B9KZNCjuCVyksLbZpGEUHojXYgiYL1dA8ESUF9AinTc6+c51WMFOR13F7RiIKr70Hpwh2yU8mCHaDkz73F1z+ElBnXw5qax75k5Uh/AOWlRfvx48fFVIwiWtntdhH2jRbyah+KkGL79u3IzstHmCMGhoxSmHIqJSdj9lBQMnQmz3dZZWSVQxOfBaPdhYaGBnbFr3YvUqC+M4YUhAXZzj/++OMYNXo0UtIzkJqRhdRMqSkbianpcEXHIlynxxCNDma7E/HJqTLKyBJ1Ut1Z2Tk4//zz8dFHHykgJi5CTQTOKFLQXPLPf/4z3njjDWGARUZYchI5s1q6dClMJhM0Gg1qamqwe/duWWV46qO4ezQvpX26fAwuBM4oUtBCy7PIIhWd3EQ2M6TWo+ioOp0Ozc3NeOedd2SXQ/VS3ANqi1yryMHVfc7M1p5RpAhURLSQ8hVHm0DiI3QQYFJ4yZpJ4QVGCJ8yKbyEz6TwAiOET5kUXsJnUniBEcKnTAov4TMpvMAI4VMmhZfwmRReYITwKZPCS/hMCi8wQviUSeElfCaFFxghfMqk8BI+k8ILjBA+ZVJ4CZ9J4QVGCJ8SKd5//31MnDgRZCVLFg47duwQMSfUhiUgK1klGsukUALFwV8GkcKztZXMfSwWC9auXRu0WNm9Icak6A0d/k0VBMhWjWJsU3yJlNQU6G0a6E1aNDY14s033xSbjNS0Z2NSqCJ2rqQ3BMiQk7adNo1vgj3WiLxpZkTm6BAdF4Vf3rFcxMomQ0+1joBJQcMesZi2JPqTvv32WzF3pDkkzSVpTkmu3AkEf8qjtlCb+BgcCJCsaJ/3kluXICk9ASkjjSI6UeUVHbGyR40dKcIN0zRbLbkGTArqvBRSiTaeHzl6VHY6fPiwCDpuNpuh0WpRV1eHhx9+GEeOyC/r1VdfFYs18ljHx8BHgDo5jRK/+c0BVNdUIybXgur5FuGDtuVXVqSO0SEuJVpERDpx8oT4o1SDGAGTgnbePfXUU5g16zzU1tV1phGorZOWhldXIzsnF+ERGgwJC4MzMhLlFUNlllOH2to6sftv3rx5wqnuwO8S3EKaCdAoMfeKuXDFOpA31SpibFM8C/LyV38zxco2oKSsBI+2P6pY9NO+kA+IFMRaWiDRfoj8omLoHFEwJeXAnFYgOZlS82FIzoUmIUskfVIOTCl5ku+nukwpuTDEJMPicgtvcBQlk4+BjQD1HdoYRrssKcZ2VL4BI2+xo60zWKSIlb3JivzpRthjTLhkzmwxraZ7gj1aBEyKv/3tb2LnXHZRCexDG1Hw8/tRtmiPqqnkxm1InbmAvXkMbB50aR117I8//lh473AlWJA/szPG9qOdDpn3OoUP2tG/sCKqWIu0rBRs2rRJ/AkHWxOlGClyisvgqp2Kilt/jerVz6uaht1xENmX3AFrZjG7uOnS9QbmF+rUtHBes2YNomLdSKwyo2GFjxjb7U4RL49iZdsTDJjQ0ox333tXeDkP5mihHClKKuCuJw+B+1X0DnhE1NXhIXAVewgcmBw4rVXkoIycTQyvHgZLjA4VP7Ng2vbOkMJesSYoyAuF7aJY2Qk1OrjjXVh558pTsbJPK1ihC0wKhYDkYqQhQKMExdgmhUhktFOoYJvvtna47fcRY5uCPLbtciveEbkAABVzSURBVIBUtI4UHSqqyvHM4WfEaBGsaRSTQposOZdCCJD7ofb2dpSUFsOZ6omxbes14hERY+K9NqSPM8DiMuHyuZcJDSOpc4NxMCmCgSqX6RMBWgfQi9mfXvRTuGIc4s1162Y7RBiwbtOm7vHxpu+xd8TKTolAVm4GduzcIcJ2BWNtwaTwKT6+qDQC1HkpxvZ9992HnPwcxBabMW5lR/RUUr92J0H37yJW9jY7cqcZYI0yYlrbVBGemNYnSk+jmBRKS5/L84kAWT6Qa/xJkyfBHmMUi2sKCC+FEB6CiFjZ622ILtQhPikOa9auAXklV9ouiknhU4R8UUkEaJQg16orVq5ASkYSkutMGL/OJjvGNo0W9KZ76FwzrLE6NE1oxHPPPSdGICWnUUwKJaXPZZ2GAHVW+ic//Oxh1J9Tj6gsK6quMnXE2JYwbfKMEp7Pme12TLjXJmJlJ6bHYdHNi4RDbTIZUYoYTIrTxMgXlESAOisZjM6/dj4iY53InmgRMbbJvsnfGNukoq25wYzIbAMqh1di/xP7xctAqkuJg0mhBIpchk8E6J+bbJUoVENhSSFcWXqMWGjFtB3y1hKeUcLzSeuQSQ/YkD3ZCEesGVdefYUIW0wqWiVGCyaFT3HyRSUQIK0QxQqZOnUqXPFW5E41iM4sFtc+XtR5On2fn+1OocY95xYLogo6YmWTUSppt5TQRDEplJA+l3EaAvSPTdsK7rnnHkTHRiG2xIQxyy3i7bS/0yZvstDagt5xFJ5vhDXWgJbJLfjTn/6kiF0Uk+I0cfIFJRCgxTU5Ijhn5DkwuXQou7hn+ybvzi7nfOYjDoy704KYci3csS5suGeDcHQQ6GjBpFCiB3AZXRCgTkkq2IULFyI2IRqJw41icU3vGUitKqfj95qX7KJ2OlB+qRHWBB2G1VThhRdeCNguiknRRZz8RQkEaDvwEweeAAV2d6YYUXuDVVjBKjFt6k4SoaLdYEXKKB2sLhOumX+N2M0XiF0Uk0KJXsBlnEKA1hK083Hu3LmITnAju8WM1k3S7Ju6d3ip38kuasRNZlgSNCguK8Qjjz4C2vzmryaKSXFKnHwSKALUCckKdsuWLSgqKUJsoRmjl1owfTftolNw2tTNeJBGiylbSEVrgDPOigsuvEDETaR1jT/rCyZFoD2B7z+FAHVCsoKdMXMGHLEWlF1kExoiOfZNUkeH7vlmPGxD42obogr0SE1Pwb333SusaKlNcg8mhVzEOL9PBGiUIB9epIJNy0xB4jAjGlfbha1SMNYS3UlBC3h601022wJLlA6t01rxyiuvCLWw3GkUk8KniPmiHASo09E0hTrhmDFj4E6zoHyOGVO32pTVNnWbNvkixvj1NiRUa5GUHo9f/GIZPv/8c+FUT87zMCnkoMV5fSJANkc0Sty06CbxviBznEXsqw7Evql7h5f6fdoOG4bNM8KVYUBdfa3YukpumOQcTAo5aHFenwiQfdPBgwdRWl4q9lHXXEf2TTax71qNqdMpwrQ7RZ0T7rUgo8kAV5wd1994PU6ePOmz3T1dZFL0hAxfl4QATZvIvun8888XnTBzgkHsp6YtprTAJq0TzfdVSVTXox3rmLoFFuGkuaAkDzt37ZT0LJ5MTAoPEvwpGwGPCvaBBx5AfHw8HEkG8XaZbJxIE0QLbfmpQ4vUcb//ZdQvtiBphA5mhwGTWyfLejYmhSy4OLM3AjRK0BbTpqYm6PQ6ROiHwOAOgyk2HOZ4/5MpLhyUAiojNhxa+xAMiTgbJrPJu9l9njMp+oSIM/SEAK0lKAQXkaKsrAzFJcUoLi1CcVkxSsrlJbonJz8bjkg7wjRhiNCFIyk1CQXF+bLLorqpvOLS4o42FRf39Ag+rytKisgR/ekhcCV7CPQp4uBdJE8aZK5N1rAvv/wyXnrppYDSnj17UFNTA41GA5PJhKVLl+KZZ54JqExPm+SgoCApyhE5og1Dl+5D7dqX1UvrXsLwVc8g+1ImhRzBK5GX1hSkjiVykAEejRyBpHfeeQfNzc2gmHcUxGfbtm3CFDyQMj33ynle5UhRXApHVTOK5m9E+S3tqqbSm3YhbdZNsKbls4NlOdIfQHmJYMePHxdeyCmild1uFyEeyBGz2odipMjOy0eYKx6mnCpYCutkJXNhHcyFtZ1J3r1Ulzm/GtrkPBgcbiaF2j1IofrOGFIQHrQvlnyDVtfWIjouHjEJSYhOTJacIuMSYHW5EaYzYIhWD4PNAVdsvOT7RV1UZ1wCkpJT0NbWJvtljUJy5WICQOCMIgXNJz/99FPhlOrAgQOQm9r37sWCBQtgNJoQodGgsqoKpPd+wo+ynnzySbHoI6LyMbgQOKNIQbpqIgYtaMiWXm766quvsHXrVlitVrHAIvUe6b5p07vcsmjHF7WF2sTH4ELgjCJFoNDTQorck9DCihZYLS0tYsFFIPEROggwKbxkzaTwAiOET5kUXsJnUniBEcKnTAov4TMpvMAI4VMmhZfwmRReYITwKZPCS/hMCi8wQviUSeElfCaFFxghfMqk8BI+k8ILjBA+ZVJ4CZ9J4QVGCJ8yKbyEz6TwAiOETz2kmDhxoniJSy9zaQOTXE8cSkAYkJWsEg1gUiiB4uAvg0jxxhtvoKGhQZj7WCwWbNiwQUQ/VfvpmBRqI871nYYAEYKMOO+66y5kZGZAZ9FAZ9SJ8MK08chfn7CnVSTxApNCIlCcLXgIUKf/3e9+J+ze7DFmZE00wZGhRWx8LFavWS0crSkV5FHKUwRMCmI5JbJM9SeRy3SaO3oMAmlOSU56CQR/yvO0R8rDc57+R4Dk9eWXX2L58uVIzUwWMbbHrbKh/FIzLDF6jBs/TmxLIKtpyqvGETApPC4TP/jgAxw7dkx2Onr0KFasWAGaQ2p1OowcORL79+/H236U9fvf/15spA8kYIcaoHMdHQhQJ6dR4tChQyIMWEyODcOutmDqVodwqJZUr0NCWiwWLFygeKzs3mQQMCloz8Phw4dx8cUXY9y4cWiQnBoxblwjRo0ejcKiIrHBaEhYGKKio1FbV9dZTqOM8sZhwoQJuPHGG0Ukm94emn8bGAjQTIBGiXnXzENUvAu5k61ovtsK8kFLHsTJy58724ihVUPx+L7HFYt+2tfTB0wKUpnt2rUbhcUlYo+0KT4V5sRMyckYnw5dbCoi3IkIdydCF5MCuianDFN8OgzueNhcbowfPx5//OMf+3pu/n0AIEAj+mOPPYaC4gK4cww452bbqRjb5P5y8kYbcqeYYI+2YO6Vlwu50j3BnkYFRApqHK0Jtm/fjpyiEtjLxiLvirtQcsMWWan4+ofgSSU3PCTrXqqraP6DSGmbD0tKLsY2NICmcnwMbASo75CbfNpT74q3IW+aAZMftAlfsMIpc6ez5FG3WeDO1yIrNwPbd2wHqfBphAnmoQgpyD9PTnEZXLVTULGkHdV3PovqO59TKT2LYb98ClmzfwlrZjF78whmb1GobCKEiLF97z2IS4hFQoUZo2+3ikinXbyUtztFvLyiC4ywxxsxZdoU8YdHW5+DOVooR4qSCrjr+9ND4Cr2EKhQpw12MaScefXVV1F/Tj0sUXqUz7Zg6jZ7h+v+boFZyHs5xcqOr9QhJiEK6+9ar0is7N6ekUnRGzr8m+II0D88xdgmhUhUrFuoYMevs0G47vcRY5uCPFKsi4qfmWBP0qO6rhovvPiCcJQRrGkUk0JxsXOBvSFAUx9SuVcMrYAz2SRibNMo0WXa1G20oNgWpJVKHWWALdKCedf8HJ9/8bnw3NJbXf7+xqTwFzm+TzYCNEpQjO05P5sjwoDlTDZh8kaHUMGeikbUjRCe69N3d8TKtiZqkFeYi0fbHw2asSCTQrZo+QZ/ECBC0DutTZs2oaCoANH5Joz9pU1ET5USUrgjVrYD2ZMMsEWZMeu8WXjv/ffEyz+lF91MCn8kzPfIRoDeXL/77rtom94GR4wVZRdbRUD4mY844BkN+vqc8YgDjastcOfpkJyWJMIT0ysBpe2imBSyxcs3+IPAX//6V6xbtw7pWWlIHO5fjG1PrGyyi7LG6NHSOhFHjhwRI5CSowWTwh8J8z2yECAtEQVPob0SURlWDL3chClbOgJF9jU6dP+dplq06I6v1iI5I1EEdiFfxlSHUsRgUsgSL2eWiwB11q+//hoLb1qImAQ3ssZb0bTW3rG49qGC7U6C0763O8VLvuHXmOHONKKmrgZPPvWkeBmolIqWSSFXypxfFgJkq0Te4MsqSuHK0KPuBhumbadQwnbJa4nuxKB1yMT7raDwxM5YG+ZfN19Y0ZJzbSVGCyaFLBFzZjkIUAf97LPPMGvWLLgTnMieZETL/Z1vrv0ZJTzq2nYnpu/pUNFG5mpRWJIvVLRkOqLEaMGkkCNlzisZASIEhUbYuGkj4uLjEFtkxqilltPtmzwdXeYnqWjJijZ/hhG2WCPaZrThk08+EW+6Ax0tmBSSxcwZ5SBAatK33noLDeMaYHIaUPJjc4/2Td2nR1K/k2lIwworYkq1wi6KCPjtt98GPFowKeRImvNKQoD+qUkFe+tttyI+KQ4JlSY0rbF32Dc96vR7LdGdLB67qNKLTLDG6TBi5Ai88spREak1kGkUk0KSmDmTHARocX3w4EHU1tbAmWRG9fwOK9je7Ju6d3ip34kY49fbkDRCD5vLggULbxQGh/Sy0N+DSeEvcnyfTwRolKCA8/PmzUNsYjSyms2Y9IA0+yapROiSj1S0uxzCsNAcq0F5ZRn27dsn7KL8XVswKXyKli/6gwB1Qlpc79y1E+UVZYjOM+OcW6yS7Zu6dHYZC29S77ZutiNjvB6uOAdmX3Ix3n//fWH+4Q8xmBT+SJ/v8YkALa7JCvaCC86HK86O0h9bhYZI2DcFooKVQJAZD9vQsNIKd64emdkZQutF/gP8sYtiUvgUL1/0BwEyztu4cSMystMRV2FEwwq7mNqQzZK/o4DU+zx2USU/McIaZcDMWTOEG04aueSOFkwKf6TP95yGAHU88gXb3NwMd6oVpReb0PpQpyMCCf/0Ujt/b/lo0d20xorYoVqkZiVh5cqVwoWOXE0Uk+I08fIFuQhQpyMvG7ctvU28L0gfY8W4Ozv2SgRD49QjMdqdwoSk8gojXGkmjBozCs+/8LzwFyXnmZgUctDivD4RIJuj559/XjgtE/uor+nZEUGPHVqh0YTWLxM2WJHWYEBknAM3L16Ejz/+2Ge7e7rIpOgJGb4uCQGaNpHpNnmIdMc7kdFowIQNnhd1nXuvaU2hUiJNFKloa64zw5WlQ2lFMdr3tkt6Fk8mJoUHCf6UjQARghwRbNmyBUlJSXAmG1FxmQmNq22YcI+lM9G51OS5p/un1Pt/qHfUMguS6vWwuEyYMWOGrGdjUsiCizN7I0BrCfIQP2nSJBgMBmhM4TDFhcOaEg57ekS/JmqDIXIIwjRDYLNZvZvd5zmTok+IOENPCNAosWvXLuGVMT8/H9m52cjOy0ZOfjZyC+Sn9KxU2JwWhGuHQKMPR1xirHCX6U9Z1AZqS3ZONrKzs3t6BJ/XmRQ+YeGLUhCgBTb57aVFNtk6PfXUUwGlzZs3o6qqChERETAajVi0aJEw2Qi0XLpfzqEoKSJHtGHo0n2oXfuyqmn4qsPImbOS3WbKkbwCeWlNQYZ3NGKQ+5pAEm0Qevvtt9HU1CRi3lmtVmzduhVfffVVQOV62iTncZUjRXEZnMNbUHLjNlQue0LVVLFkLzIuXAJreiE7WJYj/QGUlwh2/PhxEeJLr9eLyFY7d+4U7z/UbqZipMjOL0B4VDIsRfWwlY9TNVlLx0CXXgKDK5pJoXYPUqi+M4oU9Cbz4YcfRkVlJeyRbtijYmCPjlM3UZ2RbkTHxmLy5Mk4ceKEQqLiYtRC4IwhBQFGG0pOnjwpnObu2LkTHWkXduxUM3XUS+R89tlng+ZjVK0OEor1nFGkINNcWmjRQolGjf5M1AZqiz/mwqHYEQfSM59RpBhIwHJbBi8CTIrBKztueZAQYFIECVgudvAiwKQYvLLjlgcJASZFkIDlYgcvAkyKwSs7bnmQEGBSBAlYLnbwIsCkGLyy45YHCQEmRZCA5WIHLwJMisErO255kBBgUgQJWC528CLApBi8suOWBwkBJkWQgOViBy8CTIrBKztueR8IUOemRJ4+5CbyFN7S0gLvnXfkJFluOZTf044+muvz54B23vkskS+GLAJksv/nP/9ZxKegPTZyEm0Me/rppzFmzNhTe7QpGP2xY8dkleOp86OPPhL7aoggcg8mhVzEOH+PCJCTgVWrVmHGzJlobW2VlSa3tmLM2LGIi49HWHg4NFotyisq0DxhgqxyPPWSx0Ly4kGOC+QeTAq5iHH+HhEgn60XXngh3NExMEXGwByTBHNssuRkik6E1hWLMJtbJF1kHOianDLM0Ykw2p3IyMzCgw8+CAoPQFMpOQeTQg5anLdXBD788EOce+65cKTnI6n1KhRctQGF8+6XlQp+fh8Krr63I/38Pln3Ul05c1bBVjISiWkZuOeee/HNN98wKXqVGv8YVAQo1t3MmTPhyC5F1uzlqFr+W5BPLjVT+S2PwlUzGQnpmdiwYQO+/vprJkVQpc6F94qAhxTO3HLhnI7IIBzjrX8ZtcFOnQ74yBkfOeVLyMhhUvQqLf5RFQS6kmKVGCFq1x+Bmqly2X4mhSrS5kokIcCkkAQTZwolBJgUoSRtflZJCDApJMHEmUIJASZFKEmbn1USAkwKSTBxplBCgEkRStLmZ5WEAJNCEkycKZQQYFKEkrT5WSUhwKSQBBNnCiUEmBShJG1+VkkIMCkkwcSZQgkBJkUoSZufVRICTApJMHGmUEKASRFK0uZnlYQAk0ISTJwplBBgUoSStPlZJSHApJAEE2cKJQSYFKEkbX5WSQgwKSTBxJlCCQEmRShJm59VEgJMCkkwcaZQQoBJEUrS5meVhACTQhJMnCmUEGBShJK0+VklIcCkkAQTZwolBLqSYmWHh0ByZxlsl5me8te+jMpl7DYzlPrcgH9WDynIwXLmT5eBXFgOu+Ogqqls0W44q1uRkJ7NvmQHfI8JgQZ6SGGJToAxpwqOqglwVk9WNdkrGhEem4745FQmRQj0uQH/iB5SmCxW/EeEDmfpTTjLYOlMVpxlUCHpTPiPCC3iEhKZFAO+x3ADBw0CHMlo0IiKG6oWAkwKtZDmegYNAkyKQSMqbqhaCDAp1EKa6xk0CDApBo2ouKFqIcCkUAtprmfQIMCkGDSi4oaqhQCTQi2kuZ5BgwCTYtCIihuqFgJMCrWQ5noGDQJMikEjKm6oWgj8P+us6nFZI1XSAAAAAElFTkSuQmCC[/img][br][br][size=150][size=100]Write an equation using [math]x[/math] and [math]y[/math] to represent the hanger.[/size][/size]
[size=150][size=100]If [math]x[/math] is 6, what is [math]y[/math]?[/size][/size]
[size=150]Andre and Diego were each trying to solve [math]2x+6=3x-8[/math]. Describe the first step they each make to the equation.[/size][br][br]The result of Andre’s first step was[size=100][size=150] [math]-x+6=-8[/math][/size][/size]
The result of Diego’s first step was [size=100][math]6=x-8[/math].[/size]
Fill in the table with values for x or y that make this equation true: 3x + y = 15.
Create a graph, plot these points, and draw a line that goes through them.​​​​
What is the slope of the line that goes through these points?
Match each set of equations with the move that turned the first equation into the second.
A:[br][math]6x+9=4x-3[/math][br][math]2x+9=-3[/math]
B:[br][math]-4(5x-7)=-18[/math][br][math]5x-7=4.5[/math]
C:[br][math]8-10x=7+5x[/math][br][math]4-10x=3+5x[/math]
D:[br][math]\frac{-5x}{4}=4[/math][br][math]5x=-16[/math]
E:[br][math]12x+4=20x+24[/math][br][math]3x+1=5x+6[/math]
[size=150]Select [b]all[/b] the situations for which only zero or positive solutions make sense.[/size]
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Information: IM 8.4.3 Practice: Balanced Moves