IM Alg1.2.7 Lesson: Explaining Steps for Rewriting Equations

Is 0 a solution to each equation?
[math]4\left(x+2\right)=10[/math]
[math]12-8x=3\left(x+4\right)[/math]
[math]5x=\frac{1}{2}x[/math]
[math]\frac{6}{x}+1=8[/math]
Here are some pairs of equations.
[img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAU8AAAG8CAYAAABeyydFAAAgAElEQVR4Ae2dBfTtxNX273r7toUipRQWFH9xdy5a3N25SJHCBYoWLcWLtrgUKO5O8dIWt0txp7i7Wz8c5lu/6d2HOfuf5CQ5SU5Ozp61cmKTmT3PPPvJzCQnM8xZMAQMAUPAEMiMwLDMV9gFhoAhYAgYAq4lnmP9YJizxTAwDhgHjAPxHAjvGW3iGZ6o0zaVacEQKBoB41XRiDY7Pc2XlirpE3WCoc621QknsyUbAsarbHgNemzNFxPPQWfEAJdfO8MAQ2FFT4GA5ouJZwrQLEozEdDO0MxSWqmKQkDzxcSzKGQtnb5DQDtD3xXADK4UAc0XE89K4bfM6oSAdoY62Wa21A8BzRcTz/rVkVlUEQLaGSrK1rLpUwQ0X0w8+7QizezuEdDO0H2KlkKTEdB8MfFscm1b2RIR0M6QGNlODjwCmi8mngNPicEFQDvD4CJhJU+DgOaLiWca1CxOIxHQztDIQlqhCkNA88XEszBoLaF+Q0A7Q7/Zb/ZWi4Dmi4lntfhbbjVCQDtDjUwzU2qIgOaLiWcNK8lMqgYB7QzV5Gq59CsCmi8mnv1ak2Z31whoZ+g6QUug0Qhovph4Nrq6rXBJCGhnSIpr5wwBzRcTT+PEwCKgnWFggbCCp0JA88XEMxVsFqmJCGhnaGIZrUzFIaD5YuJZHLY9S+mzzz5zW221lRs2bJhf2OaYhWQEtDMkx27u2QMOOKDFHeEQ6/POO6+5hc5RMs0XE88cINbtkvfee88tt9xyLQdgm2MWkhHQzpAcu7ln48QTAeWchf8ioPli4tkAZtx5552tFqeIKMcsJCOgnSE5dnPPiniGPRZanYin3Yi/r3fNFxPP77Hp2y0hP4SXbWsxdK5O7Qydr2hmDOFMKJ5Rx5pZ+vSl0nwx8UyPXS1jSpd9jjnmcE899ZSTVqi1GDpXl3aGzlc0M4YIZTjeyXYops0sebZSab6YeGbDr3axRSyF6CKmkN+67snVpZ0hOXZzz8aJJxyyh0bf17vmi4nn99j05ZaMTelWgxG/c3VqZ+h8RTNjiHjKDZhSyjHp0TSz5NlKpfli4pkNv1rF1q8oaQENnaFWhtfEGO0MNTGrcjNEKEO+MASEcMIp68H8t0o0X0w8K6dqcRnGEVy68tZqSMZaO0Ny7OaejRJPOWbi+X29a76YeH6PTd9tSZddPxwKRdXGrOKrVTtDfMxmnwmFUvdeOGfhvwhovph49ikzwi572N2iOOE5Lax9WtxSzNbOUEomfZBonHhad7298jRfTDzb8bG9AUJAO8MAFd2KmgMBzRcTzxwg2iXNQEA7QzNKZaUoCwHNFxPPspC2dGuPgHaG2htsBvYUAc0XE8+eVodl3ksEtDP00hbLu/4IaL6YeNa/zszCkhDQzlBSNpZsQxDQfDHxbEjFWjGyI6CdIXsKdsUgIaD5YuI5SLVvZW1DQDtD20nbMQQUApovJp4KINsdHAS0MwxOya2keRDQfDHxzIOiXdMIBLQzNKJQVojSENB8MfEsDWpLuO4IaGeou71mX28R0Hwx8extfVjuPURAO0MPTbGs+wABzRcTzz6oNDOxHAS0M5STi6XaFAQ0X0w8m1KzVo7MCGhnyJyAXTBQCGi+mHgOVPVbYUMEtDOE52zbENAIaL6YeGqEbH9gENDOMDAFt4LmQkDzxcQzF4x2URMQ0M7QhDJZGcpDQPPFxLM8rC3lmiOgnaHm5pp5PUZA86VNPDlpi2FgHDAOGAeiORDqd5t4hifqtE1FWjAEikbg//2//1d0kpZegxHQfGmpUp0Fqs62NZgrjS+adobGF9gK2BUCmi8mnl3BaRf3MwLaGfq5LGZ7+Qhovph4lo+55VBTBLQz1NRMM6smCGi+mHjWpGLMjOoR0M5QvQWWYz8hoPli4tlPtWe2FoqAdoZCE7fEGoeA5ouJZ+Oq2AqUFgHtDGmvs3iDiYDmi4nnYPLASu2c085goBgCSQhovph4JqFl5xqNgHaGRhfWCtc1ApovJp5dQ2oJ9CsC2hn6tRxmdzUIaL6YeFaDu+VSQwS0M9TQRDOpRghovph41qhyzJRqEdDOUG3ullu/IaD5YuLZbzVo9haGgHaGwhK2hBqJgOaLiWcjq9kKlQYB7QxprrE4g4uA5ouJ5+ByYeBLrp1h4AExABIR0Hwx8UyEy042GQHtDE0uq5WtewQ0X0w8u8fUUuhTBLQz9GkxzOyKENB8MfGsCHjLpn4IaGeon4VmUZ0Q0Hwx8axT7ZgtlSKgnaHSzC2zvkNA88XEs++qMJ3B3377rdtnn33SRa5JrGHDhjnsripoZ6gqX8unPxHQfDHxzFiP33zzjWOp0smjTCT/m266KeqUt2/EiBHutttuG3Ke61i+++67Ied6fWDbbbd1+++/v7e/Clu0M5SVJ3wB7zpiHpY5yr6oY+E1vd5O8oOibdN8GXjxFDF55ZVXfEtt3333jcSceEcddZQbe+yxHS2klVde2d18882Rccs+CKE32WQTt9hiiw1xSM4hQLocOPCRRx7pJplkEm//LLPM4h599NGyTc2U/ueff+6mmWYad/bZZ2e6Lm9k7Qx504m7Thx7nnnm8ZjDGzDneN0CvIFP2223nfeDLbbYws0999ze7roKKHYdffTRkX5QBr6aLwMvnmuvvbYniIiKFh0qAbIffPDBbsUVV3RPPfWUe/31192GG27oDjjggDLqqGOaZ5xxhlt88cUjSXPfffe58cYbz7366qutdBBOyjXVVFO5l19+2Qvu6aef7hZZZBH38ccft+LVYeOcc87xTovNZQftDEXmB2f+/Oc/e27dfffdHvMLL7zQ78f1GIrMP2ta2It4IvCyrLLKKu6NN97ImlTq+DfccIN77LHHUsfXER988EFvc1QjQsctYl/zZeDFE9Kw0JKDNFHiec011/hz9957r6+D5557zrfgdtlllyLqJFMazz//vPu///s/t+iiiw4RT+7EtBi4IYThnXfe8faGZaPMY4wxhjv55JPDqD3fpgxLL720O+GEE0q3RTtDkRl++umnHnMcG6wJrNnfbLPNhvQYisw7T1rYBqcQtNtvv929+OKLpQ+fMCb/t7/9LY+5Hss111wz0g9yJZjiIs2XgRdPwWzLLbeMFE9IRQtN7m7s4+C0jNiuMpDfr371K9/9xh6xSWz46KOPfBlOPfVUOeTXl1122ZCykdaMM87ohbaKcpAHC9gRWMflyw1g8803jz3fVrgudrQzdJHUkEsfeeQRj3lYR5SZ/QknnHCIMAk+JNQLfsFnxDOuTsIChrZyXO+HcZO2Ec9//vOfSVEiz5EfQ2hHHHGExzPEOPKCgg5qvph4jgZ2++23HyIwnKLbQouUCrrgggt8d5lWKl0wEYK4uuF8liUuHTlO/gg5RMceTZrHH3/c2/rQQw/JJX5Ni1O3qklj5plndox9pnGYtgQz7pA+tjLUMHLkSPfFF184HmiJTRrHQw45xMcv2y7tDBmLlRidrrnwRsrHeq655vLH33zzTX89xxi3Ywx9pplmcueff76j/EsssYRbY401hohsmCnXZl3C68NtsMa2p59+2t+4eHh35ZVXDuEGY7aM+1OXjI9+9dVXvjxTTDFF5rc7EM8bb7wxNCPVNvxebbXVYv0gVSI5Imm+mHiOBnHXXXdtOXOI68MPP+yPQxYqG9HBMX7605+66667Low6ZJv4aZe99957yPXhAR6mMID/wAMPeEJHiSddIBz2k08+CS9111577ZCy4QTEHXfccRMdtC2hHDs45Y477uguuugi7+hsr7vuur7VcPjhh3sbwDQMtJRpneGYZQbtDEXmxU1XhlcQOAJ1+MMf/tCXmSEgjh9//PH+RgJOf/3rX/05bmoMDcnNJc4ubuBR/IJLUccR5rhA/j/72c88H2j5M67OGDnpcI5APf361792//73v73tc845p2Po6qyzzvLxsFfixuUTHiftrOJJ+uuss473A/CL8oMwjyK3NV9MPEeju9dee0WS9Y477vDHeQosTs4aMV1ggQUSyfL111/7a4jfaSFuXIAkf/jDHxw2EiBQFGkYv5x00kmH2ER8uvtcI+RGuGabbbZE8SRu2iXOdgb16YITKMfWW2/tW1iUl7cC9ttvv5ZNksYTTzzhMX/ttdfkUClr7QxFZkJZebsBQRHeMJb44x//2B9DPMF2+umnb5Wflh7xETkepMCxpDciuD6KV9x0oo4TPy5wDjETW4lHXfEgVR4y8haEjJsTj7cIEFq2ebgUCq3Oh/T1gsgzxqqPsx8VwPTEE090Bx10kD/NfpQfRF1bxDHNFxPP0ahGdW05xdN1CM14kASpNI6//fbbcri0NY409dRTe5JCLMgqpBHikTllwM4oIaY7ttxyy3nC89bAoYce6oYPH+677nFkXWuttXx6pNlpueSSSyLLD1YshPfff9+3KHE4ORZ1EeUDWxyrzKCdoei8wJXuLwK0ww47+GWbbbbxZZNue4g99feTn/zE8bCpDuG0007ztp577rm+vkJbpbtOq7NTOPPMM/0wBEMTDNdQ//RAaAzsvvvujiEzHqLRI1lppZU8t7mB6vDMM8/4cfqwUSJ+AGdC+/S1Rexrvph4jkY1TjzlIQyVJA5PJbGPgyd1O8JKpnKTlijBkwqnq8Q4E05IS2Xeeef1rRK68TyZvv76631UunFRLU9JB7t5kPHWW295W8Yff3y3wQYbtMol8WRN/LSLXJO0luEDuoRJQVqe3LjKDNoZysgL/J599lmPO/W//PLLR9YR8ZZZZhm33nrrxdaHto9rkjilzxE/LtBqpKV79dVXt6LAbTjOjVYHbmyc4+2PNIG89fK73/0uU8uTHkzoB7R8sZmFm3unoa80dibF0Xwx8RyNVpx4UuFydxPyIaIco/KSRA9CZlniKk47gdz1sYH8xa7777/fE1qPeXKebvumm27ayuKee+7xcXkNq8zA2B1dc8ogGEtXlK4r41c6yNsBmqw6Xrf7ZaYP5jgz3VnpnXBs4okn9jjAIeqJNyPgCGOkjD8fd9xxrWJFDWm0TjrnH1pm4VfSmCevhiGGtDYliHhefPHF/hBcoQ7hH2vGpYV7l156qT8m16ZZ//a3v01sfOg00vqBvq6ofc2XgRdPSMwijs2aShJScI6WEoPjdDsJnJ922mn9+AvnqwzYRf4QXcRTbJBWMuOMYSA+g//zzz+/v1bKi3AliX+YRt7tjTfe2Nv6wgsv+KfH2E0ZsIHtqG4fT5uTWtB5bdHXaWfQ57vZp4xSdlrQlJcxw1lnnbX1Yjgvz4MBIsmDI7ZlqIKxdrr4Urfd2JLmWt7rROglPziz6qqrurHGGst9+OGH/jjDPfCItyXmmGMOzz/iwaHJJpssM5cYU03quSXZjZ2hH7Attidd1805zZeBF0/u3IgQr+xAXlk4JpVBxch4DET/5S9/6f9hxPEqA/ZgFwQWO1lLtx17eFJ7yimntJnFdRzjpWJuDoxl8iJ92cKJEfyTiW4VN59jjjnGvw7DvtgvGIcGMya28MILt/APzxW5rZ2hyLRJizG6pZZayreul1xySc8xhk0k8C8wcOApPPw69thj3R577OEf1Pz85z/34iBxy14j9oxJMnQAPxgfZ5GhE84zfrvQQgt5m3ldCJ+hLhk7x4+i6jLJbsY5O72xEnW9+AG+IDxijQ1lBs2XgRdPSIHosJYuMNssYaDCGLNDfBhb1OfDuGVui21icyjg2Ijw6H8YYQ/X0YWGYDhwVfZjE2OsPLBim4ch/IVU7NdYEQfB4alq2UE7Qxn5UU5aky+99FKkGHL+lltu8fVBnYAT44hV1U9YZvKE2yy8oqdvrpxnPJqyUE/8tZfX9uLqMkw7apuHR5dffnnUqY7HsCVcsAGbygyaL4WI53vvvefvUqg/zXm5WxVVkLF+0DKzqCQbmw5jmfq/7f1U2D/+8Y++daMdt4wyaGcoIw9LMx4BRJpx+n4Jmi8tVcorUHwcI2w6m3j2lgrcfRlr23nnnXtrSI7cISdjbFdccUWOq7Nfop0hewp2xSAhoPnStXjeeeed/utCtDYRThPP3tMJAeW1Jl7K7qfAGBjDCnTHqgjaGarI0/LoXwQ0X7oWT4HCxFOQqMeabm/ZA+hFl5QeTFXCie3aGYouj6XXLAQ0X0w8m1W/VpoMCGhnyHCpRR1ABDRfTDwHkARW5P8ioJ3BcDEEkhDQfDHxTELLzjUaAe0MjS6sFa5rBDRfShdPeY2pmwdJed8E6BotS6DRCGhnaHRhrXBdI6D5Urp48jReXmU677zzchXAxDMXbHZRBwS0M3SI3henedOijnMkxYHHA8J+sVfzpXTxbGrLU/5VUeXT4ZCA5IsNnf5ZgTMRl4XtXgT+YdTNRF9l2aydoax88qYr9cbMrvyzjaVTOOmkk3xjBV7UPcBH+QRdr7iZBSPNl8LEM4sRWeNW0fJMS1QqmQ8J8zk3WtR8CotPjlUVyJ8PTEhrng9o8Bc3/Y8c4slnw8Ycc0z/oQ2+jlM1ST/44AP/v/Y0jl8VhpKPdgY5Xpc1r5rxwWr57kInDBHM6aabrm/Ec9SoUf5bDeF3JOqCfZQdmi8mnqNR0kSNekcS4eGLP3xd5sknn/Sf5uLfPMyngvhWERDJiSaayP9PHXv4DzhCyj+KQhuY0mGGGWZwfEYMp+LzaBNMMIHfrsJO8sA+7MK+To5flU1hPtoZwnN12AY/6lQ+DZeEIXH54DL1DN51b3nyZSbmaaLxYeJZItuqaHlqokaJp3wDk+kSCBBUPshaFVmxC+cIv83JPouIJ7bwoeTddtutVSvE52tMfBykqsDfLJkkDNuSHL8qe3Q+dRdPsZcxwU4Y0l3nZin8iOIj/OA4XCcI5yWfqtbYwefo+Mg3wmniWSLyVYinmC9E1eIJ0fhikYgUBBDyiWhJGmWu+ScXZGMSLoJ8nZ3Ph4kd0hqlxcIxsTXKocqylW+fIuAydBAlnqFt2CF4lmWTTrcp4skXkBhGghPgDEfDugZnPsIxxhhj+EnpiHPXXXd5HvE3XvmGqMZH9qmXLItcF7dmFlhmRMBGE884lAo6XgfxhIBMAgcxGTvkQ7HyfUzOJYUsxCNu2kC+fF9UWiWSD1Mjc4w5sTfaaCO3wgor+FkOQ4dKm0eeeNjBV8JxWLkZafHks2Z02bCT7ibdOD7OzL6+ceWxIc01TRBPsOb7mzJVRpR4MibPuCkfy5ZviPJN2s8++8x/NzWp5cd01tSHXhge0MdkPwl7mQWW7y7AXxPPJLQKONcL8dTOzgyCODYLk1chRHztm6kT/vSnPyWWkrSEWOE6joBpnkyTzrLLLuvHMWUaW4yAkHwQGTtxEN52YBoIWqYbbrihP59obAEnGWdFtLElSjw5ztxLtIxxfpmOmNkmKRe2E6fs0ATxpLvOB4nBkaDFExzBk6mfCTzAY5/pPzjHtdzkkgJc1wtj7/oY+/rBZZguNjILrHzxi/xNPEOEStjuhXjixGGQKYjHGWcc984777ROIUqQkakK4kIS0aIIGJdOeBziIYrYOfnkk3sHgJwc/9GPfuRtCr8oz3St2BlO8BWmxzbXpl30tbJPy4IpmfnSOCFKPBn+kJsT+S244IK+BQQWO+20ky8Tx8sO/S6etCipe7rrcAzM5ObDPEOCoazBU4ZRiv7mbpq6olEwxRRTeFtFaEU82Q/tTJNe1XE0X+xpu6qBKGcnCl/4RnyobCpawpZbbumPp2ktyjVFrhFM/r2FbUxpAAFxKPbDh0P8QYFjtFSiAvbTjU67RE0Niy177rmnX8QZ5EkxTi3OQTwWAk6PXdLtjLKtrGPaGcrKp9t04zjJQxdmDWAIiZs4U33AT/BkSg16HoKz2HDwwQf7aaylLuR40pr80y7Ud1TADma/pPHBOCsPt+RhK2Pj2E9PrM5B88XEU9VWHFGZcgBSMhdPSLxddtnFH48jDcnHtTwRmKhFEz40kZYjwwSMV0mQcc8jjjjCOwukxFa67BK4jmO6RS3nWVOutEt4nWxzLXmsvvrq/uVn5sMRZ8bJ2Q6x4zppCUWJsaRb1lo7Q1n5dJtuHCfBMuQPPBO8aXlyDi7xgIZ65xhDPdSFcIzuPA+P4gIcYkw1btlqq61cuCDocSG0lW3sgS/YLC3nuGvrcFzzxcRT1UocUSEblczUsaEAIBQQgJkQ40LcmCeEjlriWrHkK5O/PfDAA63saGVgg8yHLuNe4RQHRx99tI/DFLNlBu0gTE6HbZSTcwSZC4p9bA2nsGX89je/+U2ZJrbS1s7QOlGTDThHnYecBLOQf2IqcTkn4ilixKyl4M9QiczWGQ6ZrLHGGq16kbSqWFMG7MU2bGZbBL2K/PPkofli4jkaxTRERZyobMhMgKA8gWdWwShC56mgpGsgGOODPDnlKSiBY3SDmLdIxJJz2MkDGAk8LKJ7RPyqApiE3XZxEP5kgH3cJCiLOA/xOR41HXEZNmtnKCOPbtLkhgM28gAQbFg4poVG4kociQfm9EQQTFqPzN3+P//zP36f6bMZy686YDtlYAntpQx1DpovJp6ja4sWEpUpf4WTSg2JinNTwYzXQERaTIzx0f2oKjz66KP+Fan//d//9TYwVsQ0vbyQHjoUT1B59w87KRMtjC+//LIqM/3NRF5FEixZ48ynnXaad5of//jHfr7yueaaqzWFLeNeYTnKNFg7Q5l55UkbHMAL3klLkm0WHcK4co3EY81NTPbfeOONtn2dVhX72BIu2FxVvectn+aLiedoJEPyJRGVCuevmYgTLydT6VUH8sRGxquYRjjOBt7rIw7v1BG/6oBd4CV4ip0c440FmY642yls85ZLO0PedOy6wUBA88XEczDq3UoZgYB2hogodsgQaCGg+WLi2YLGNgYNAe0Mg1Z+K282BDRfTDyz4WexG4SAdoYGFc2KUgICmi8mniWAbEn2BwLaGfrDarOyVwhovph49qomLN+eI6CdoecGmQG1RkDzxcSz1tVlxpWJgHaGMvOytPsfAc0XE8/+r1MrQU4EtDPkTMYuGxAENF9MPAek4q2YQxHQzjA0hh0xBL5HQPPFxPN7bGxrwBDQzjBgxbfiZkRA88XEMyOAFr05CGhnaE7JrCRlIKD5YuJZBsqWZl8goJ2hL4w2I3uGgOaLiWfPqsIy7jUC2hl6bY/lX28ENF9MPOtdX2ZdiQhoZygxK0u6AQhovph4NqBSrQj5ENDOkC8Vu2pQENB8MfEclJq3cg5BQDvDkAh2wBAIENB8MfEMwLHNwUJAO8Ngld5KmxUBzRcTz6wIWvzGIKCdoTEFs4KUgoDmi4lnKTBbov2AgHaGfrDZbOwdApovJp69qwvLuccIaGfosTmWfc0R0Hwx8ax5hZl55SGgnaG8nCzlJiCg+dImnmP9YJir64LhthgGxgHjQC85EN4E2sQzPFGnbQTdgiFQNAI4oQVDIC0Cmi8tVaqzQNXZtrTAW7z6IaCdoX4WmkV1QkDzxcSzTrVjtlSKgHaGSjO3zPoOAc0XE8++q0IzuCgEtDMUla6l00wENF9MPJtZz1aqFAhoZ0hxiUUZYAQ0X0w8B5gMg1507QyDjoeVPxkBzRcTz2S87GyDEdDO0OCiWtEKQEDzxcSzAFAtif5EQDtDf5bCrK4KAc0XE8+qkLd8aoeAdobaGWgG1QoBzRcTz1pVjxlTJQLaGarM2/LqPwQ0X0w8+68OzeKCENDOUFCylkxDEdB8MfFsaEVbsTojoJ2h8xUWY5AR0Hwx8RxkNgx42bUzDDgcVvwOCGi+mHh2AMxONxcB7QzNLamVrAgENF9MPItA1dLoSwS0M/RlIczoyhDQfDHxrAx6y6huCGhnqJt9Zk+9ENB8MfGsV/2YNRUioJ2hwqwtqz5EQPPFxLMPK9FMLgYB7QzFpNo5le+++87deeedbosttnA333xz5wssRi0Q0Hwx8axFtZgRvUBAO0NVNgwbNsydddZZjrWJZ1Wod5+P5ouJZ/eYWgp9ioB2hiqL8e2335p4Vgl4AXlpvph4FgCqJdGfCGhnqLIU/SSeDDNgryxV4hTm9c033zhsYelF0Hwx8RxdC88995yjcsIAWeocsJcljZ3EuemmmyorTuhwvSJ7p8JqZ+gUv8jz1Ec/dNvh1x/+8Ac3/vjju3nmmccttthi7vHHH69UwLDhwgsvdDPPPLObaaaZ3LzzzusefvjhIqsjVVqaLyaeo2G74YYb3AorrOD22Wcft++++7qVV17ZTTLJJLUck8LxLrjgAjfrrLO6scce2y244ILuxhtvjBVRxOvoo4/2xK9CyLAPDKeYYgo30UQTuTXWWMO99NJLqQhaZSTtDFXm3Q/iiY1rrbWWO/LII1utztNOO81NO+20QxoaZWGHDX/+85/9jebrr7/2oo2QzjbbbO7RRx8tK9vIdDVfTDxHw0SF0BIIF45VITaRNRVzEHtE4N955x137bXXunXXXdfbffLJJ0de9eCDD3rhpNWQtTxXX321e/nllyPTjToI2VdaaSV30UUXeQc79dRT3eKLL+7te/HFF6Mu6dkx7QxVGtIP4vnEE0/4esPWMMwyyyzugQceCA+Vtv3xxx/7RsyKK67YygN7xhhjDLfZZptl5nMrkRwbmi8mnqNBRCgRJVpwdAk+/PDDHPCWfwldGMiLrULqSy65xJN84YUXdtydw0CcNddc0y266KK5Wp60PMAkbXj++efdDDPM0Gbfnnvu6e3bddddK2uxpLFXO0Oaa4qIww2MepFuu9RjXNqcp94JXMt2p2vi0spy/P777/c2Uv/hTZebYRZOZMlTx33kkUe8DVtvvXXrFLbAsQknnLASHCRjzRcTz9HIIJ577bWX4JS4hrhCXiFzSK7Ei7s8iePMN998fhGHwpapp57ajTPOOG3iyfGjjjrKHXHEEblbnlnFU8i+zTbbtDBiPBmhYChEcAMGttgdlzcAACAASURBVFkEO9bh+S6h6ni5doaOFxQUYb/99vPjdwxpLLPMMm6XXXaJTBk85pxzTjfxxBP7+AzVHHPMMX7skaEQqf/Iiws4+NFHH/kbNXUHD6jHLbfc0vckOtUTtmdZ4sxlnJ78d9hhh1YU8mb8leNvvvlm63jZG5ovJp6jEUc8ubudccYZbu211/Ytp08//bStPiADXV/ueIyP0kLdf//9PZlWX331RDJnIRJxk8KTTz7pWCR89dVXnkg4Wkjqhx56yIld2J2n2w4WWVsZ99xzj3v11VfFPMd4MkRHUKVs2Ik9tGJGjhzpvvjiCzdixAgfj/FSiddKpIQN7QwlZJE7ScoPFxnPBqvLLrvMY7P00ku72267rYVT7gxSXsi4Ijdr6o+FuoFvSYEHSvSM9LL33nsPOSZx4tKj206+q666aivKZ5995n70ox/54/fee2/reNkbmi8mnqMRRzypJFpwjNdtvPHGbvjw4e6VV17xMSDzHnvs4c4880xP5ksvvdTflTfddFMn3eYkkYF0QpQ06yxEOPvss73tf/nLX1qX4XDrrLOOH5vC9m7E8/rrr2+lm2cD0eRp7ahRo/zl2Lbjjjt6nLGNbcZtaSHjYNQDccoO2hmqyI88kxaxgVYl/BMcrrjiCo/LY4895mjdc9NJemDCdWkXyVOvqRuGgfAFemXUCwtc0sND+lrs1wvX6GPsJ6VFGWiZTzPNNK3Gya233uofGGHLfffdp7MubV/zxcRzNNQIJgIq4a233vJEQfSoQCqZrgvbBLpQVB53WbphCJWckzTCdRJxoggVXpu0jbgzBooAkY6EE0880R100EF+N614Yr9eaHnS6tHHw7wkz6j1lVde6XHiKS12EHiAtfnmm/ttjtHi5xUU0uQ4eCZhGZVPnmPaGfKkkeUaegYiQFFrWplhEAxYw0PG+eRYGE9vI7CMcaddeDAUFegS0z2WRsFVV13lh16wnQZAGlui0s167Omnn3bLLbecf7uExsrvf//7Vmv4tddey5pc7viaLyaeMVDi1FNNNZUfc5I7o5CFNU+Up5tuusoIFGUmdiButARCMXvmmWfcjDPO6O/oHGeRlifbUo4wTe1wEp/1r3/9a7fBBhv4mwfjlnQduZF0CrwNgLDLDUjig60I6fvvv++HQfiftxyTeGWvtTNUkR95Ji1RNsC/ZZdd1iEcaTGijtMuUXly7IQTTnDLL798W56kSX3iG1E8krSEd2nW4l9ybdSavGhp06ghTXoyc889d6INUel0c0zzxcTTOV8ZdIMgpwQqi5dxxxprrCHdiv/85z/+VYkwvlwXt45recaRKy4dOY59tNIQHbZxKrq8rDnG+5+8pzr99NP71gPlY6E1QryoQDp6wVFokevj2J0UKO9cc83laAHLtWJfeB2vWtGSYXyv6qCdoer8k/IDs5NOOsndfffd7vXXX3fjjjuuO/7441uXgBlxygyrrbaa55LOgzHspZZaKjb/uDHPuOEqOBYXKOOvfvWrthsH45yUH25VGTRfTDxHiydPNBkYF0IiDggnx9gWMvMwhG4MlSdk5hwtrKR/PUCQOPJEHU9qYZAfQrTVVlt5u4iLjby8zDm2w0UeKNGKRNSIkzYccsghfmwybXzikTfdrPPPP9+LOfbxkEMeGPHUlq458cAFLGX8DtvYryJoZ6giT/KgG3rYYYe54447zj/Bjsr39NNP9zicc845nmdgIt3nv//9727bbbdtaxFGpdHtMakb6kkC9TP77LM77KsikB+t3Pnnn9/zBS5hF8NknR5cFW2f5kuLpWP9oLVZdJ5dp1e2bVTQzjvv3CInBssDJHmNJCTz4Ycf7okNmalM3l+k+8x22YE86DLTZeEfRowVMnzAg64FFlhgSCuZ+JAf5xPxzGInrzoxHpw2kDatWxyMGwrDB4g69kmLlwcQ2PPCCy/4fx+xTR2w8FSVLw5VEbQzVJEn+DA+zYMOWt3UXZQQcYOZdNJJ/ZAJLS9usLzlwZsJdFlDQSvLbuqDfCebbDK30UYbtcY7GbKqIn/KBV780QL/whbeWYb/VQsntmi+tBSzbIHqpoKrsA0i80QPYjCuh0Pzl0YIRBAy868GnH+TTTbx4kC3WJy/mzKmvRZ7yC9qQbRCYWQbwiGaYXyOpQ0QNYt4ymtJYX6yLfkiFgwh0K3nvUXW7E855ZStoYe09nUTTztDN2mlvZb6YzhF3oyAY6usskpbvUlaCBRP1rmGhRYrf0II61jilrUmL1q61BNvdTCOjS1VBmzg4dWxxx7rv4Nadf5SVs0XE09BZvRTYFqctCipLE1STWaeUr7xxhuVk0mcKWodFMdv6jiUQZdLXxPuZxVPnZ/eJ23yZ+AfMWCb92lpiWEb8asK2hmqyleEk/x4zY0WuoX6I6D50rV4PvXUU26OOeZoa9nwlewiQxUtzyLtbVJatDp5Et/EoJ2hF2Wkxc0YnoX6I6D50pV4RgmndNHOO++8wtAw8SwMSksoQEA7Q3Cqkk0+9cYfL6psbVdSsIZmovnSlXiC0SmnnOLee+89Dxd/m+IJMALKmv0igolnEShaGhoB7Qz6fJn7PC3mPUqGLRgLzjKUUqZdlnY8ApovXYunzuqAAw4w8dSg2H4tEdDOUJWRO+20k7vuuuv861m8M8wDPWt9VoV+/nw0XwoVT1qgvN9Hy9O67fkrya6sBgHtDNXk6tqeD+AriKe1PKtCP38+mi+FiWfYZUdApSuf39Tvr7Ru+/dY2FZxCGhnKC7l5JQQSr0kX2Fn64CA5ksh4hm2OIsWTkAz8awDdZpng3aG5pXQSlQkApovXYtn+MQ96iGRCCuvMxE3TzDxzIOaXdMJAe0MneLb+cFGQPOlK/HkfU55NUmvpQUaxsk7DtrP4ikvfvfDAwG6ktjJkmYMjnhVzshZtOtqZyg6fUuvWQhovpQunoPa8kRY+HgDNxVehOZmwl/tENM6BuzlZe3JJ5/cz3jJXwZvv/32WFMRV/7K2s8PO7QzxBbWThgC9t/26jjA3w15f0/+DilfqOHrQmladdVZ+t+5hBBC/k30wQcf+A8982FehJ//qkcFvgqPcJp4RqFT/2NhL4MbZy9Dp/w5Lz24Xtqpb7ZdtTyrKkg/dttpbSI+4RdzpBVaN/GMmvGST6Fhb9SMnMw3tMQSS/ivJ5l4VuUFxeWDEDH3Fl9n4kvx1CHf4KwyIIgsfK+ULyZFDf9wXr5uBhfHHHNMd+ihh/as8WHiWRFDmLKAjxLz/UwCX6WBAAceeOCQypc7q5gmxJL9stfhjJcyrPD22297e5mRU45hB7YxbQZfl7eWZ9k1U3z61B9fBONTg8Izpkjhs4FhPRef8/cp0niAO+S55JJLep5FiadMdMdkglxz1113ecHH3l4EE88eoM5nvBjzRIj4Z4kECMG3Qccbbzz/XUc+HszcSBCLb3WK8Er8cM21WZfwer2tZ7xk5k3Efv311/dOJvGxj8/w4WgmnoJK/6z5khX1inCGgS87PfDAA+GhUrfJHw7JcJYWT7jNN0T15IN8DpKWai+CiWeFqEMQPnzLh4G5w9LdlQA5ePtgkUUW8UR+9tlnPamZ+uOTTz7xswPK9y/lmnDN+CTn9cIHh/Ux2Q+v77TNV99xMr7lKOHzzz/3H2HmQRJlM/EUZLKvwY+FABcQEtnPnlr6K+6//35fr3SHyVcCw0xawORcmes48fzyyy/91+IRynfffbdlAjMQ8OHyXgQTz4pRxymYYx0SML5EF5mAoyCUzEtNkLEdvpoNiSGzTE3hI6gfcTjSDxe+sB3uh9sqidhdbOSDvbvttlvLwciPrwAJcbHfxDMWwtgT4Ei983V2ZgGgt8GQDmPIa6yxhq+72IsLOPHRRx/5aS24MfKtVj7yzfgnrbxO4o3tWZY05saJJ70uGgLYyayjfGP34osv9n6Bzb0IJp69QH20WCJIdI9EMEOyConoVvUyyIyXTC2C8Ergm55TTDGFH0rgOOQW8WQ/LItcU/e1doay7UV4mOiONxnA669//asXB2YjlfE9eFB2YDpoeIgwsTCZW6dpLeImdeu2pyO8l/mZwrKDEc8NxE6+RMXULb0Kmi/2tL2EmuB//kwOx+yHEiCCPIFn9r8wcI4pNJjnh+00gUF0Wqhplyhy6nwQxHDGS5wd58AmZupkzJYbAPOH04qmPMylxHgu8fotaGco235uMsOHD2/Vscxpz42JG2qn3gb1kHaJKwt1Ssttww03dHvttVdLmLgRdhJQ7NcLnNHH2Od4miDiGTVkQDrwi3mbQrHvZGeafPPE0Xwx8cyDYodrHnzwQU9KZv2DAATWP//5z/1xWpeMazLRGeOREI27K90oCewnTYTGnEvEj1v4q2y48IQ8KWAfIkg3EgfFyTiGU7HPdrhAYGzkPPYTp9+CdoYq7A9xQji4EYXH4mxAYLnBpl2YIiYqML0MNz65mdL6pVtMXcJF6r3KECeeYAK3sInAUJL86YQ/cMDFqoPmi4lnCTXAvEaQkW6GBB6ycAzyQwzeb2N/xIgRjhfO2YZIBM4zq2JVBMFhxCkhbLjw8rx2bvaxDZuJy3bVTie4drPWztBNWlmvBcNlllmmbT7yTmlwTdolLi0+wLz88su3nSbNhRZayM9cynZcoJ7TLllbniLmkveHH37o+cWfNsLA2x7wLu93MsK0sm5rvph4ZkUwRXwIyAMgCElFr7766r7bse666zppEUBCunDrrbeen06VmQGZWpZuCtfw4npVIc2Ml2ILIiniip2ySAtB4vXDWjtD2TbT22DmBbB6/fXX3bjjjuvnbpd8eZKcJF4Sr5v1aqut5scRdRpwgNeA4vKPG/OkLFGLNAR0PnpfWp5aPBnaimpASI+nF88GNF9MPHVtFrjP3ZcHMLwwzzgTghkG9m+55ZZWa4LBcNkP45W9jcMkLTp/HZdyWMtTozR0X3obPN1mTJwbj/z99Y477nC8HlY2jiJWIRepT16nC/8NN9T6Yo8Ih8QecJBj5MQYMMNe//jHP1oZgw1CLb231omKNkw8KwLasqk/AtoZyrb4lVde8YLJO4z0QuhtMAEc49GMh4eCVpYtCBQCxKtSvJ608sore5sYnqkifykXNtCDkZ6LrDlOwM7LL7/ctz55GwCR5WElPTXpvUlaVa01X6zlWRXylk/tENDOUIWBCJT0LhAIup8M0bBdVaAFx9Ntuso83Pz0009Lb/HqslFesGAtDxzZ1i1v/iaMnSwvv/xypQKvbdZ8MfHUCNn+wCCgnWFgCm4FzYWA5ouJZy4Y7aImIKCdoQllsjKUh4Dmi4lneVhbyjVHQDtDzc0183qMgOaLiWePK8Sy7x0C2hl6Z4nl3A8IaL6YePZDrZmNpSCgnaGUTCzRxiCg+WLi2ZiqtYJkRUA7Q9brLf5gIaD5YuI5WPVvpQ0Q0M4QnLJNQ2AIApovJp5DILIDg4KAdoZBKbeVMx8Cmi8mnvlwtKsagIB2hgYUyYpQIgKaLyaeJYJtSdcbAe0M9bbWrOs1ApovJp69rhHLv2cIaGfomSGWcV8goPli4tkX1WZGloGAdoYy8rA0m4OA5ouJZ3Pq1kqSEQHtDBkvt+gDhoDmi4nngBHAivs9AtoZvj9jW4bAUAQ0X0w8h2JkRwYEAe0MA1JsK2ZOBDRfTDxzAmmX9T8C2hn6v0RWgjIR0Hwx8SwTbUu71ghoZ6i1sWZczxHQfDHx7HmVmAG9QkA7Q6/ssHz7AwHNFxPP/qg3s7IEBLQzlJCFJdkgBDRfTDwbVLlWlGwIaGfIdrXFHjQENF/axHOsHwxzdV0w3BbDwDhgHOglB8IbRpt4hifqtI2gWzAEikYAJ7RgCKRFQPOlpUp1Fqg625YWeItXPwS0M9TPQrOoTghovph41ql2zJZKEdDOUGnmllnfIaD5YuLZd1VoBheFgHaGotK1dJqJgOaLiWcz69lKlQIB7QwpLrEoA4yA5ouJ5wCTYdCLrp1h0PGw8icjoPli4pmMl51tMALaGRpcVCtaAQhovph4FgCqJdGfCGhn6M9SmNVVIaD5YuJZFfKWT+0Q0M5QOwPNoFohoPli4lmr6jFjqkRAO0OVeVte/YeA5ouJZ//VoVlcEALaGQpK1pJpKAKaLyaeDa1oK1ZnBLQzdL7CYgwyApovJp6DzIYBL7t2hgGHw4rfAQHNFxPPDoDZ6eYioJ2huSW1khWBgOaLiWcRqFoafYmAdoa+LIQZXRkCmi8mnpVBbxnVDQHtDHWzz+ypFwKaLyae9aofs6ZCBLQzVJi1ZdWHCGi+mHj2YSWaycUgoJ2hmFQtlaYioPli4tnUmrZydURAO0PHCyzCQCOg+WLimZIO3377rdt3331Txu6faLfccovbbrvtHOUbtKCdYdDKb+XNhoDmy8CL5zfffOOFI0k8OHfccce5448/fgjaXP/111/XWny+++47b5+sw0Jg/2yzzeZuvPHG8HBPtpPqQGyX+irCQO0MRaQZlwZ2Sxni4vT6uNhHPbBddSBPwakX+Xcqr+bLwIonBNl2223dsGHD3OKLL+6WWmop98gjj/jK0yBeccUVbuWVV24TSK6/4IIL3BxzzOHTQIBOOeWUtjg6nV7sQ0ZazJNPPrmbaqqp3FprreXFPrRl1KhRbrLJJnMPPfRQeLiSbXBkufvuu71tN91005B8pQzTTjutG3vssd2CCy7oiNetg2lnGJJxAQco2+GHH+7GH398z5PFFlvM3XzzzQWkXGwS7733nptzzjnd9NNP7yaccEJ34IEHdo1vFgufeeYZjw/+yLLLLru4119/PUsSpcfVfBlY8bzvvvu88MmdbosttvCVdtttt7WRhlblIoss4q688sq2ytl8883dVltt5Z566il35513esen0hEnHKbogFDss88+bbZ1ygPbV199dYfosE1Z99tvP7f11lsPsXGnnXZyYNCtIHWyKTxPXogJ9i255JIefy2exAFXbgDvvPOOu/DCC714coybVTdBO0M3aUVdi+2HHHKIW3HFFd2TTz7pvvrqK7fxxhu7gw46qFKco2wLjz3++ONuvvnmc8ccc4znCFgvuuii7o033gijlbaNv6y55pr+hghH2ad+EXJ4W5eg+TKw4klrkwo6/fTTfd0w9sc+x0MBueaaa9zEE0/c1iKlcmeffXY3cuTIlgi98sor/nrSwMmLDiIiWYT5H//4h7cJZ5VAKxMbOReGl19+2Y055pi+BRgeL3ub8kjLEru0eL744oveXoRdyn7uuef6YwsvvHBXzqWdoeiy3nPPPd7Oq666yidNOSkjrSopS9F5Zk0PO9Zee203YsSIlk2bbLKJ76U899xzWZPLFZ8hI3BhEd/bf//9/X4dhpOkUJovAyueEBqHlDvb7373O19ZYXeFivztb3/rNtxwQ8HPr3EC7tRUNl19AnHpunOMLmgYRCCEGKyzOg/XkHaW60488UR/Da01CXSFSGfTTTdtEZVzpD/zzDO3biYSv6o1rR3s0uIJvhwHb3AncHPi2DjjjNOqvzx2amfIk0bcNdQT/PrhD3/o64x9MKYMUXXIMTmeFC8uv7zHTz31VI8lIiU2YKNgnTfdLNdRXur/T3/6k7+MfXok3Mx1HYmNxCGwFtyy5JknrrZlYMUzBO/dd991yyyzjHfG6667rnWKShk+fLjvzrQOjt6gG/boo4+2HZbWLK0lAhV77LHHuvHGG893Tc866ywvDjPOOKObcsop3Q033NB2fdIOtiAYWYgignTZZZe1kv7www99OozV6rQY191rr7283a0LIjYoV5YlIokhh8RWLZ5EBGfwlkD3FywYo9NlkDhp1toZ0lyTNg7iM80007hf/OIX7tZbb3U//elPHfV+0UUXtdkMjkcffbQfU59pppnc+eef77v6SyyxhFtjjTVKFTHy3n777T2W119/vVt++eW9HTvvvHPHfLPUv8RNix1Czo2R1nAo4i+99JIfTsDPttxyS/fFF1+4ddZZx9sPf8inzKD5MtDiiePtuOOOvgvOmBuVEQbAwknpuncKODdx11133ZZzMIbEeB75SPeTFtSbb77pWyTcXdMGiJFVPKU7dMQRR7SykWMIuhYeHIkuXEjY1oWjNxgfY+w1y6LTiNoX8cS+TuHss8/2WBx66KGdoiae186QGDnjSYZBqK9ZZ53VYwWmjI2PO+64rVfeqFPe4JAu81//+ld/DT0AusxcDy5lBfKnvsmHXhOtfG5MjIvT29L8CO2gNxPFgb333jvyOA9XOwXi8MwAe/bcc09vi1yDLUsvvbR/KwS78Vt87cgjj3TkyTVJ9ko63aw1XwZaPAESUiN8kGjeeedtdcM5x8MgKoV1UiANKh0xFOGhIrn22muv9ZfyNJN9ukmc4+5JKyQqQA7ihAvpcj3DDOFx2Y5Kh2uwKRx24AEGgh4lnieccIKbZZZZWmWISpNjpKsXeSAVdTwunfC4iGdUyzOMhyhhI/EpezdBO0M3aelr77jjDl9ftD7BhEC9Lrfccv74Rx995O3noYiUg4eS1DGtz8cee8xzRPduwnyk7tOsw+tkG3vocZEndS9BbrAXX3yxHBqy5lpd1+wjvlHHBYMhCQUHKAc8It9JJ53Ui7BgwxCI3EjImzcuuMmQLg87i+BDYErkpuZLY8UT0BmY18snn3wSCYy0HKmQjz/+2MehWw2xIERcoCIRTp5OaoJIxXMtY6yk1UmIiQsRVlhhBS96vMDOnfWoo47y3cDPP//cffnll22LkCrKRsQbscRJll12WSettqhuuzhNUnmj8ijiGGUAnyTxBF+EkxaPxjqPDdoZ8qQRd43ceENewBW6m5STFjwh5AgY/OQnP3GffvppXLKt44graaddnnjiida1soE9G2200RDchQf4DnF6EeA7OFHXBOwQWxBYzm222WaVmqb50mjx5O4ULvPPP78T8eQp+0knndQCHxLLmOW9997rj7/22mu+kuIEj2uoXB6+iDOzr1uUxOPVpqmnnrrNWVqZqw1IwjXhQvqMzWZpeUqylPlf//qXT08cgzu5kFHi0frgfU/ySArYknbplJbkI+KJfVEBLOgdnHzyyb4c2M5NRZch6tq4Y9oZ4uLlOU7LEgcPx2UpA4LEcV1OznGDW2+99VKXKeRHp+2oMoAd45vYE960pNGAP8Thy/G0HJB4UTZw7IUXXvB+xFoC9mDXqquu6utbjrMW+7p9VS1MM8225kujxTOOUDKexEvjVCyB9c9//nNfYU8//bQ/huPzwnDUmCfkwXlZuJZ98mOgn7s8+4zhIKY8pJlgggl8C1UqiXEl7UByLmpNen//+9+HECkqrhzDHsbTwpbpYYcd5svIazQ6MOa5wAILJOaRdcwzzFvnF+4niSfloHXPQw22wQLMGT9kP2/QzpA3najrsIshE15zExuxm/duEQXeyOCmxjAOHOGdSsrDP9kkwBG5Vo4VvWbsEnvCh5dygw278jrfuDFPyhK1MBQRF3j3FRtohEiQHhI3eTCgBwUe1Ltw5fnnn/fR8dff/OY3cmlpa82XxopnEoLyug5P6iTcfvvtvgLpBglhWeMAPPjRgRYQd2bOh4u8PkPFQggqX8a/REhIlyebECFtwPF4jUpsS3Md4s8Ngq4/13MtY27YEZUOT9s32GADHzdN+kXEwS4WcQicGNvEPjkXYizbK620UiteHlu0M+RJI+maM844w3NAbsbUN0Mo/LON8iGgcARR4MFRKGJwZptttim9LuTBFv+CkgDf55lnnkz8lGvzrKX1G/bY4Dp4nHbaaR4D/mjAPmPAvIUAB8ATHOEtb7KUHTRfBlI8AZw750ILLeTH0Hhyx1gaT+9kLIqKIB7d7fCBC8dxaOJTmXoR8eVaCIhj8EI9LQpasXPPPbcXNF5fyRLIc7XVVsskFlwDMXkiSWuAbiEiFdWVJi7jvbvvvnsWs7qOi104gsaR4wTpounz7BMHu/MG7Qx504m7DueGU9woGXL42c9+5nifWPB/9dVXfbkZxyYer7Xtscce/h9g9IKy3FzjbEhzHF/ANlr38JqhLnDvBts0+UocyskfHxBGuuL4G6/yIeL4EXYgotQ5jROOzzXXXG799df3vtXt8I3Y0Wmt+TKQ4ikgQWL+jsmrPPfff38kWXnRfKKJJhpyjkqNWyR9SME/l3gABQF4XYl9rssauJ4nkFmvxQa66IgmwxVxDklLmZeSo7rzWW3NEp/yYBNr6oM1izguazkWtc6Sl46rnUGfL2Ifmxm/Q6B4KKnxZ184QVxaqdQF21UGhpZo+dHixSbBvyobKC8PKhn35BsL+qEZ5/lzBPhgG+d5NiGcqcJOzZeuxfO8884b0mrgWJFhrB+0zCwy2VRpUWm8wqT/257q4gIjQRgEsCxSM+7EuFHVTlsgRJmT0s6QOQG7YKAQ0HxpqVIegeLdRXlvTXerihTQPLYVWauMR0l3vMh065IWr1ExFif/jKqLXWXboZ2h7Pws/f5GQPOlK/EECv41IeGzzz7zXxpCSA844AA53PW61+JJa2yHHXZwBx98cNdlqVsCdNEY67z00kvrZlrp9mhnKD1Dy6CvEdB86Vo8QQOhDFueRQon6fdaPLEBAaXb3LTAeBsPM8oaDqgzXtoZ6myr2dZ7BDRfShFPuvJ06YsKdRDPospi6dQHAe0M9bHMLKkjApovhYinFDQcAy2y9WniKQjbukgEtDMUmbal1TwENF8KFU/gkqfvRbY+TTybR8Q6lEg7Qx1sMhvqi4DmS1fiSUtT/j1BkcOWJ1NU8ABJjvEhirj/iHeCy8SzE0J2Pg8C2hnypGHXDA4Cmi9diSdiKBOghQ+M2Jan8KzlXN7Xl0w8B4egVZZUO0OVeQ96Xjyg5CGsrPsBD82XrsSTv5fx4QkRR9a6u96Uliev9LDU+SVyISI21tlObAu/4tMrx9HO0Cs7qsxXQG2VxgAAIABJREFUuMGcW7w90os3SPAjvnAmusGEhP/5z3+qhCFXXpovXYlnLgtyXNTLlicVzdeR+CK4THvLV2fqJk7cpHgXNWmK4RzQF34JAs+0E/yfne1eBu0MvbSlqrz5HgBfjZdvM1QtntQ53+rkS/HSGOF7Dwip/Oe/Kiyy5qP5YuKZgCAVDdkgGP+r5bNYfMCBiuarSmU4v+SZJW1Ix5dl+JcQ25CSD5JETTGcUNxKTj344INeOE08K4F7SCbwihu/fHauavGEm9LilNk5ZaZMOFvnYOKZoXaoaO7QCKi0NC+55BJf+Xz3sow7JflALskvjbmIOteEUwzLWHPWrzelyS9vHMrE/Nz81XXQxRMs4BcBQWM7S53nrQO5Tj42XLV4kj+zZPJdWWkgyFe1wm+KEg88WCSeCL+Uoeq1iWcGxCE0E7aF095SgXwRHrFiKoQwSGVzjHh5HII0soonc7hwDV/ukSDfLOWDH0I+OdeLNeWiu8YXrHCWQRVP6oKvy/ORZGbLZEgITPiINh9KFkEtu46yiid2Z1nS2j9q1Cj/mTk+MceXnSTAFzjCN3NHjhzpJ2eU5ysIfi84beIptZNyzWfEWCRQqXxgmIVtAhXJx2SZVG2KKabwE3jhFPxnHIfI0kIlblbx3GSTTfw14ZfpZYphCCh2ShnCdRaH6IawfGaM75EiDoMqnuDHB5L5XiZ1wpTQ1DUfzJZudFiHYT0VvZ1VPOl9ZVk62UvDg2+X8hlExuqZtkQC2PCNXRoDYCYzZXKTwc+y+oek2+3axLNLBPliNZXHLJQiPLyCtcgii3iHePbZZ/15PmMnH7vN0jWCOFnJwUc9uCbs9ogzJoln3JQafFw2zlHywEeZ+Go/451gNqjiyY1j+PDhrZvZFVdc4esNIWHaXzACq7jAubRLXBpyPKt4ylg6Zei0pGkswAPi8f1QHmDxLIF0CfCEj5ATiMfYPa10znOcsdEknPyFJfyYeHYBKpW3yiqrOKYEkIqmEvlivMy4yd0SIUNQ+ZMA3Y646WMhhnYGaXmy1ueIHxWwhdZMKNIyxTD2JhGNa/VC3voY+xzPGrCZD0rLeCz7gyqeYCd1wZr6CqceTsKWDxUzVpxmCXkQl2ZW8YxLp4jjvH2Bz2A3/JCFtN9//30/A0PUhIVF5J0lDRPPLGgFcalQvj7E1B3iAHI63IcAaaePpYVX5BTD0003XeuBjLSQuWtje5kBUWW6D70guM8884ybccYZvfCKIIt4sh9iV6aNUWlrZ4iKU9YxMGNaFCY9S1s/YJV26WR3VvGMu6FKnYbrpJssZaX7HU4IJ7aEQ2FivzwMZbij10HzxV5VSlEjEJbugszkxyV0a6n0MBAvy/SxEEk7A8SLm2K4k5NFTTH8l7/8JTRxyHZI+k7bcU7B8XCKZ7Z5CZr0wI33YyeZZBLfyqKVTmuchVYUN5BeBe0MZdtB/TBHDxO/8UCP2TL50DaBuqX11amOi7JRBCtNK5U844Zxoo4npSlzEUXNlCmtcF5homsOf0gLXKT3hr+w34ug+dKyopcvoncCope2UVk4OP/VZ1sEj1YolYtD0MqDRFHTx1LRV199dacits6Txz/+8Y9MLbK33nrLv+cZkpZXQRiM5/3UuBA35hnlEBwL0w/TxOa4RQsy89SACa1PRJfrehW0M5Rth8yWiYAwISA4yAOiv/3tb5XMlin8DcWTOqqqHuQhGe92SpCZMuEY9vGGCNgwnxEzZbKNfZxjHvcqZsoU28K15ouJZ4iO2qaymFFQupnhWqYYFodgJr+o6WOXXXbZTK0JSMLn/LKQWR5SMcUwgWv5myxilyUdVfzCd8ETRxXxZJtjvQraGcq2g79EUnYW+MJbErxHzFsZvKkBHmWH66+/3vNZ/mEk9sDtKuqCMiKS00wzjZtsssn8GxismTlUyn/66af7ngmvL8lMmfRUmFGThkwVdkbVg+aLiWcUSqOPITxCLr2my0klMtMhfy/jSSlPDSEBY4+8mzb++OP78wlZDDlFnnmmGGa+dUhJixiiIZxx3ewhmVZwAKzk5hNiic29CtoZqrADgQhny3ziiScqnS2TesAGeCYtf7ZZqgpiAz0fsOA1JY5JYJveVDhT5n333deyW+JVvdZ8MfHsUANCrKi1XCoOwRN34vFeKOM2eQjJNXmnGGYIgaey4hxiX13WGkPsDJ2maju1M1Sdv+XXXwhovph41qz+EBMGy3spKjWDpDRztDOUlpEl3AgENF9MPBtRrVaIPAhoZ8iThl0zOAhovph4Dk7dW0kVAtoZ1GnbNQTaENB8MfFsg8d2BgkB7QyDVHYra3YENF9MPLNjaFc0BAHtDA0plhWjJAQ0X0w8SwLakq0/AtoZ6m+xWdhLBDRfTDx7WRuWd08R0M7QU2Ms89ojoPli4ln7KjMDy0JAO0NZ+Vi6zUBA88XEsxn1aqXIgYB2hhxJ2CUDhIDmi4nnAFW+FbUdAe0M7WdtzxBoR0DzxcSzHR/bGyAEtDMMUNGtqDkQ0Hwx8cwBol3SDAS0MzSjVFaKshDQfDHxLAtpS7f2CGhnqL3BZmBPEdB8MfHsaXVY5r1EQDtDL22xvOuPgOaLiWf968wsLAkB7QwlZWPJNgQBzRcTz4ZUrBUjOwLaGbKnYFcMEgKaLyaeg1T7VtY2BLQztJ20HUNAIaD5YuKpALLdwUFAO8PglNxKmgcBzRcTzzwo2jWNQEA7QyMKZYUoDQHNFxPP0qC2hOuOgHaGuttr9vUWAc2XNvFkfvS6Lhhui2FgHDAO9JIDoXy3iWd4ok7bCLoFQ6BoBHBCC4ZAWgQ0X1qqVGeBqrNtaYG3ePVDQDtD/Sw0i+qEgOaLiWedasdsqRQB7QyVZm6Z9R0Cmi8mnn1XhWZwUQhoZygqXUunmQhovph4NrOerVQpENDOkOISizLACGi+mHgOMBkGvejaGQYdDyt/MgKaLyaeyXjZ2QYjoJ2hwUW1ohWAgOaLiWcBoFoS/YmAdob+LIVZXRUCmi8mnlUhb/nUDgHtDLUz0AyqFQKaLyaetaoeM6ZKBLQzVJm35dV/CGi+mHj2Xx2axQUhoJ2hoGQtmYYioPli4tnQirZidUZAO0PnKyzGICOg+WLiOchsGPCya2cYcDis+B0Q0Hwx8ewAmJ1uLgLaGZpbUitZEQhovph4FoGqpdGXCGhn6MtCmNGVIaD5YuJZGfSWUd0Q0M5QN/vMnnohoPli4lmv+jFrKkRAO0OFWVtWfYiA5ouJZx9WoplcDALaGYpJ1VJpKgKaLyaeTa1pK1dHBLQzdLzAIgw0ApovJp4DTYfBLrx2hrqi8e2337oFF1ywruZF2rXvvvs67G5S0Hwx8cxQu88995z75ptv2q6oO0GwFxvrbmcbqBXtaGeoKNtM2VBva665prv22mszXVdFZLj19ddfR3Jr2223dVtvvfUQf6nCLskD+4T/cqybteaLiWcGNG+44Qa3wgorOO6qLCuvvLKbZJJJ3M0335whlWqiQpq11lrLDRs2zC/LLruse+SRRyKJXo1F9ctFO0MRFsqN6pVXXnH77LOP54lOV+Lcfffdvo5uuukmHaW1D88222yzWtUb9l9wwQVulllmcWOPPbZvFZ9//vltNn7++edu0kkndWeccYb77rvvWuWpYgP7Lrzwwhb3J5poInfooYd2bYfmi4lnhtoMK0REiWNVkyONyZdccol3XEQU+xZbbDFPpttvvz3N5QMRRztDEYVee+21Pc5LLrmkXyN+Oug4ceL51VdfuTnnnNM9++yzOome7m+++eZuq622ck899ZS74447WjfpI488ss0XzjnnHDf33HNX3vq89dZbPfavvvqqt+f555/3jZ6jjz66K9w0X0w8M8CJUNKauPHGG93DDz/sPvzwwwxXVxcVsVx88cU9gbCVcMstt/h9jtdR7KtD5/uctDN8fyb/lrQqEU1usFHiqePEieeJJ57ou+x1qi9sn3322d3IkSNbLc2XXnrJl5XyvvPOOy3wsHvppZd2J5xwQutY2RvkudFGG7nrr7++LauLLrrIcdPqBkvNFxPPNoiTdxDPvfbaKznS6LPiIOxSYdICTHVxAZGuuuoqt8UWW/gxKZL73e9+5wl+9tlnF5B65ySk/EJW1hyrU9DOUKRtSeIp+UicKPEEqwUWWMCdfPLJEn3IWjDmRFUcg8fzzTef5xLDQJL3bLPN5o8xFBEGOEhLtaq6Zwx23XXX9UL55ptvtkzZb7/93M4779zaz7Oh+WLimQFFxJNBcMZxuItB/k8//bQtBUhMF3nCCSf0XYWHHnrIt1a5K2+//faJXRiuzbK0ZZyw8+6777plllnGj1G9/fbbCTGLOYWjgAGtXFooX3zxhRsxYoR3LjCjjHUI2hmKtEmEkXVckDjSOwjjUU9wZtSoUeFhv605Ri9o//3393ivvvrqiRwbkliOA08++aR79NFHW1dS31NNNZVftEgecsghnguIblLIwvsk/pD/3nvv7bEDP7C9+OKLPTY88O0maL6YeGZAE/GkQqaeempHN2DjjTd2w4cPdzwcIFCpe+yxhzvzzDP9nfbSSy/1grXpppv6Y1wb1coQEzg/5phjugkmmMBNOeWU/lrSX2KJJfzDqfXWW8/fxXfYYQe35557ymWxa4jEnZ9uFnfjxx57LDZuUSfIc8cdd/QD9uDBNnkfccQR7vDDD/f4aQcrKu+s6WhnyHp9UnwRxjTiyYNIHXB6+IBQhQFMd911V3fWWWfFcixKjMM0it7GFmxFKLWwXXbZZb4hwfhtUmA4LMuSlJbwHptY1llnHffCCy8kXZLqnOaLiWcq2P4bCcFEQCW89dZbvnJwECqMuytPuEUcEA4qD9Gi20AlyjlJI1zT5SCNtEt4bdw2adEyQXjnn39+99prr8VF9bZhX5olLpEHH3zQCzzncSRa6jPNNJMvE903cEjCIC7dMo5rZygyjyzieeWVVw7JGkGFO/QawnDvvfdGcuzxxx9PxbE0dStxwnzjtuHXKqus4lZccUVfxzreE0884cvBw5ukUCT3sWmnnXbyjRseuImIdhLwJPs4p/li4tkJsYTziAPdFSqICiOIMLBedNFF3cwzz9w6lpBU6adwOkiU1K3jzo/NaRae5kcFMJHWx/vvv+9bHbR+5VjUNb06pp0hjR3U8y677DJkwfnDkEU8zz333PBSvy3iqdPlpObYdNNN1zo2JKHgADf/NHVLnKQWsyRJnTJ8tdBCC8Xmj63wLqp1LekUuSY/ejr0Cqmr9957z5cFGxB58dM8eWq+mHimRBHQGcOjCy6Bipp33nndWGON1XowI+cgPRXGO3ppQ1F3Xyr5sMMOc6effnorayExNumuoEQiTtpFrkla82I3+TFGXMegnSGNjfCAf/uECy16LXJZxJOn6jrQUgM73fIM4wnHQk6G56O209Yv8ZIC57nZkrcIEvt6WEpanp3Esyju8wYMuOnWPO+lcpzXq/IGzRcTz5RIQpCJJ57YP2kUYnEM4eTpI9scP+mkk9w999zj77RUFnd7Aud4qfjpp5+OzZH44447rh/vnGuuudxSSy3l7+xbbrmlH0vVY0JxCdF1Ji1axWLryy+/7I+NM844Qx5yxaWT5ziD8nTNwUMERB4uYAt21SVoZ0hjF2WIW8LrpexJLTiJw/uROtDF5KGjvtGRt+bY8ccf7y/nXCeO6Xzy7JMPD2V484R6pgXKMVqh7IeBMU/qvNM4rOZ2p/0wj3D7vvvu8/nJcwg5B57YkeR/EjdurfnSYvJYP2htxl3bs+N1sA1y8KpDSAJ5gEQ3jkBLjwrivTZ5OMIdFXIdcMABnlxVdF9ff/11bwdjrBLkPU8eNpVpA90lMGCAfo011vDbYEeeq666qn/QITb1eq2doQh7KCeLCCNrubFK+jrOgQceOCQO1/DGgn7aHnKMh3AiTKTJg6Ru32UUG5PWxx13nO+FYV+4cGPWLXAeImFjFW95YPMnn3ziGw277757WxEQY4Yj4GLeoPnSUsw6CFRcoepiG93QaaaZxq200kr+6Tek4F8LUiG0umQMFBHZZJNN3HLLLedbkMSVeHHlLOo4+dBt4S6LwPM/Y/5Gh3NpcheVp6SDczO8Qcv5mGOO8Wv2eXuA1gpOXpegnaEIu3BSBIUWIHUuC8ek7FFxfvGLX/husNhAHfKAjVZmGKI4Rl7TTz+9z6tsjpG+lEmvEScpo9jMeDfvq5Ztl+TH+vLLL3czzjijW2SRRfxNjL9QMw7KEEI3QfPFxDMjmnSJESRaoLyEG5KFbVoM8h9yCMNT0DfeeKNS8kiRsOWDDz7wrRf++cF+2QEMeAsB4Wab92DpSpF3lQ6UppzaGdJc0ykOZZSycqNinyXkSZo45MNYKE+xw2vZJv2QY4hClRyTMkWtQ3ywlaGnqDHdMF4Z27R0+UMILX9a70VwX/OlMPHkqRatLLkb3XnnnYVhUpeWZ2EFsoRqgYB2hloYFRiBw/NgqtNrPsEltdpEvGgVd/uKUF0KpflSmHgypifCydrEsy5VbnbEIaCdIS5er47TcjvttNP8y+e08vop8FUlhm5o+TUlaL4UIp4IJYLJl1ak9Wni2RTKNLcc2hnqWFJan/zR4J///GcdzYu16eCDD/YfNek30Y8tUBkvyX/22WdeNOeYYw7f2jTxTILfztUJgX4QT/BCgHjo1k+BxlSThBPsNV+6bnmed955vtVJtz0c97SWZz9RfTBt1c4wmChYqdMioPnSlXjytj4tTlqbCKeJZ9pqsHh1QEA7Qx1sMhvqi4DmS1fiqR8ShQ+M2KZVWkSwp+1FoGhpaAS0M+jztm8IhAhovpQuntIapYWa93+lJp5hFdp2UQhoZygqXUunmQhovnQlnhoiEUpanTLmKU/iu2mJ9lI8+UeHfsG2aQPhuh7L2gdHsKsLftoZyiq3pdsMBDRfShdPEdR+bXnyNRhmzOQvdbyzVucZM+tKUcSSv4jKsE5dZvLUzlBX/OLs4h9M8i+muDhlH6du5aZYdl69Tl/zpVDxLKtwvWx5ysc/xPFZcyz8y1xZ5a5juvztUnoVae3j75ncfHAycOP/zuDY65k8tTOkLU+v4yFYPE/gP+PgyPxBp5xySqUteuqRWSqZ3gUbZHrfKnoV5MGSZnpnvnDGB8qLeFlf88XEs4MnIJQ4Pv9lr/OMmR2KUdhpPrEHHlkC7yjiYPJFKvnCE8d7eRPSzpClTL2My9epmJ6Fz9VxI0McwDecxaBs+2677Tb/DyI+N4iQyfS+Rx11VKaseQ4ivEh7IV+Oorx88IN1lDBKnKQpoNPmJ/E0X0w8BZmYNeLZLzNmxhShdVju2BxAtKQl2IqQYiOPeCbN5GnimQL0IAp1yMwFfBWdD7AQ5MPJCEk49W9wWaGb1BnfmOW7rWGAG4gWNqYNfKksSvySrhce89WyOPGUOKQdFycpj6hzJp5RqCQcQzyzzpiZZTZDiJhlSTA19hTp80k0mdEzi306UfDg03Z5Q9UzeSbZqZ0hKW7UOXFQzoFxFWN/5MG0FwhCmql/o+zu9hg2MBMsPQc++kHZCXytnW/eZhFPpnPJKp5iPwLeSRhNPHv4oWbEggrqZsbMpG4JXeAsixAn7Rpid5rRM8k+nQ948A2DrAGHogVf5UyenWzMK55gSuuPmQWYowrR4Nul88wzj1t//fW9iHbKu5vzzA3FWF4YZGjkxRdfDA+3bWN3lqXt4mCHurziiiu8X/CdWD5ewiSHfEPzmmuuCWJ23oRPecUTATfx7IBxLx8Y0RWhgiWknTEz7WyGPC3lTp52ETvSrkk3HAuTGT3T2Cctq3ANFszBHh6T7U42YQutJa7vNJNnp7SKOJ9HPBEf5mTiU3GUW6aZWHrppf384J2cuQi7dRqMfZIvH/zFpriASGW5USelxTnSIl9ZGJ4BnyyhG/GkB9QJb2t59rDlqYkAOeRr8YgBQUjGmq9pp53NUKeddx876C7pBWHuxj5El/Kw0O2XhS+cb7TRRn4qZR5e8OoR59J+qTvNTJ55schyXR7xBGse1kidSwuMlhc3BlqAMmdTlC1cl3aJul4fIy3qCfylvnUc2Y+7Uccdl+ui1uRLngg2072IgNKLiRPQqHLTakeEo85F5Rseoydj4hkiErHdq5YnjoIzhLMTUsmdZswM40cUp+1QHHHJO2ppu3j0DvHC2RzZjprRkbwgW1r7ogh98803tz41ps9H2cZXt5igLJxOguvE2fQEZ1FplHUsj3hiC/ZLoGUzwwwztB2Tc3pNL0ZuRp3WCGKngEiRP2nBgaqC5CvT+8Ir5saiTieffHL38ccfDzGFGyu+tOaaa/rpRXbbbTfHZ+v4yjzi+eWXX7YtTNnS6WacplWZJs4QY2MOaL7Y0/YYoDgMIbPMmMldFwLp2QyT/paapRtF3KigRUzvy2yLeezT+d11112+paOPx+2HM3mKg8tMnmD1zDPPxF1a+nHtDFkzRDR4z5GbUVxrS6ep6yZpX18b7nMdfAhbnOwj0HEh6406rkzk/ctf/nLI9L60vqlTehZRIaqs/ImGJepcVBrhsTTCmCZOmGbStuaLiWcCWlRonhkzpetS1WyGCUWInNGzG/sYo0rTKhKbmFsHhwpn8qT1yjHSAeNeBe0MaexgdkZeSEeomKWUqaLlZonYUK4qysRL8ginPO0mzyWWWCKxtYaQYHfaJU48uQmON954/iX1EDOO07pMaiyE8dnmI8+8M5onpBHGNHHS5q35YuLZAbk8M2ZWOZthB/Nd0bMtZhVPnJpr5PUaum3gw3TNtIR6GbQzpLHl7rvv9gLJE2ZEE7HkL7yE6667zm2zzTapW6Fp8ouKw0MqRArxDBem/q1iviDqlL8pM71veKPgpsyDM+lhRNmuj1199dX+AZw+nrSPqJNvKIzkGdqSJk5SHlHnNF9MPKNQUseyzphZ9WyGytwhuxCrqNkWs4qnGINQ8o4nzvLaa69lcjBJo+i1doY06fOXQASThYdmjM3x/ix/OR1//PFLLxeiwM1HbAjXjH2GApKmPHnjUJ+M9dJ9R8R4aEgrvNM4pc4PPhx77LH6cOI+LWduGhoHjklrOU2cxEwiTmq+mHhGgGSH4hFgXCtpXC3+yvqd0c6Q1kJuRvzFFKFi4f/+/D1RHDdtOnnjSb5R67xp5rmO/GltsjCOzX7WgHgeeuihmS4jH2lpIuKCQ4h/mjiZMi1jGo6sBuSJ36un7XlstWv6B4G84tk/Jay/pdyMZdij7tZqvljLs+41ZvaVhoB2htIysoQbgYDmi4lnI6rVCpEHAe0MedKwawYHAc0XE8/BqXsrqUJAO4M6bbuGQBsCmi8mnm3w2M4gIaCdYZDKbmXNjoDmi4lndgztioYgoJ2hIcWyYpSEgOaLiWdJQFuy9UdAO0P9LTYLe4mA5ouJZy9rw/LuKQLaGXpqjGVeewQ0X0w8a19lZmBZCGhnKCsfS7cZCGi+mHg2o16tFDkQ0M6QIwm7ZIAQ0Hwx8RygyreitiOgnaH9rO0ZAu0IaL6YeLbjY3sDhIB2hgEquhU1BwKaLyaeOUC0S5qBgHaGZpTKSlEWApovJp5lIW3p1h4B7Qy1N9gM7CkCmi8mnj2tDsu8lwhoZ+ilLZZ3/RHQfDHxrH+dmYUlIaCdoaRsLNmGIKD5YuLZkIq1YmRHQDtD9hTsikFCQPPFxHOQat/K2oaAdoa2k7ZjCCgENF9MPBVAtjs4CGhnGJySW0nzIKD5YuKZB0W7phEIaGdoRKGsEKUhoPnSJp7MFVTXBcNtMQyMA8aBXnIgVOY28QxP1GnbJoCrU200xxac0IIhkBYBzRcTz7TIWbzGIaCdoXEFtAIVioDmi4lnofBaYv2EgHaGfrLdbK0eAc0XE8/q68ByrAkC2hlqYpaZUVMENF9MPGtaUWZW+QhoZyg/R8uhnxHQfDHx7OfaNNu7QkA7Q1eJ2cWNR0DzxcSz8VVuBYxDQDtDXDw7bgiAgOaLiafxYmAR0M4wsEBYwVMhoPli4pkKNovURAS0MzSxjFam4hDQfDHxLA5bS6nPENDO0Gfmm7kVI6D5YuJZcQVYdvVBQDtDfSwzS+qIgOaLiWcda8lsqgQB7QyVZGqZ9C0Cmi8mnn1blWZ4twhoZ+g2Pbu+2Qhovph4Nru+rXQJCGhnSIhqpwwBe1XJOGAICAImnoKErdMgoPliLc80qFmcRiKgnaGRhbRCFYaA5ouJZ2HQWkL9hoB2hn6z3+ytFgHNFxPPavG33GqEgHaGGplmptQQAc0XE88aVpKZVA0C2hmqydVy6VcENF9MPPu1Js3urhHQztB1gpZAoxHQfDHxHF3d33zzjWP59ttve0KA7777zuct654YkTLTXmOV0syO0bQzdLyggAjw66abbiogpc5JPPLIIw4+haFX/A5tSNrOwq0qscRmzZdGiyfgsrzyyitun332cfvuu++QeuP8hRde6IYNG+aXMccc0x1yyCFDSDfkwgIPQJj555+/ZcPWW2/t/vOf/xSYQzFJgdWGG27oJptsMrfooou6jTfe2H300UfFJN6DVLQzlG0CQnb00Ue7xRZbrJKb9M477+w222yzFveXXXZZN+6447o777yz7KJmTh8fuOCCC9yss87qxh57bLfgggu6G2+8MRanEEt9g8icecoLNF8aLZ5rr722F6RJJpnEr6PE89Zbb/XnXn31VS+Yd911lxt//PHdaaedlhLS7qJR8UceeaQXcAiEQM0999zepq+//rq7xAu8Grs22WQTt/322zvseu+997yAXnPNNZlywUEoZx2CdoaybXrwwQe9cFYlnvBdGgWsZ5hhBnfLLbdU2jBIgyk+II2bd955x1177bVu3XXX9baffPLJkUmEWJp4RkL034N5px7G4cXpIY8WT0DfaKON3PXXX9+WOy0qhLeKgJAIwZ977jmPp3YbAAASIklEQVSf5f777++P7bffflWYkCqPE0880Y0xxhjuww8/9PGxlZvSRRddlOp6iYSTDKJ4wsM111zT33CqFE/wvuGGG9xTTz3lPvvsM6mGWq3hwyyzzOIFFJwIl1xyifeBhRde2N+sQ4M1liaeITpqO694SjJbbrmlrwgtnrSg1llnHS+U7777rkR3iBZdnqrCn/70J3fYYYe1WgQ4F4IK6cMAaViELKyFbGG8orfJg9YwdkmeHIP0YkvaPPOKJ/mxSH5iR9p8o+JV2fI86qij3OGHH15py3OPPfYY0mCIwgEsqUvwJci+YB11TZHHyHu++ebzC9sEbJl66qndOOOM0yaeHNdYVmWn5kuju+1SwXQ1o1qeVMTee+/tz80555x+jOXiiy92iy++uJNWoKSh11RYlkVfH7c/atQoT5i55pqr1cojLrYiXrPNNptjTBT7aDVLucok0BtvvOHzIX/Ejzy5IfFAImtgzFQcJO21L730ki879TJy5Ej3xRdfuBEjRnRddu0Mae3JGu+hhx5yq6++ui83GLJQn2WHtdZay4sndQbPGdvX2GMHnJp22mn9eDbdYeky77DDDkPihzZn4X8nfj755JOORcJXX33l6xe/DLGKwrJT2pJmt2vNl4EQz1133bXlaBpAKmaLLbbw5xEFWqIvvPCCjjZkH0JmWYYkoA489thjbvfdd3c8sIK04YMYbNxxxx09+SEK5+edd17/8IEWK3Zrp1DJd7X78MMP+zwQr3POOceT+eyzz/bHsj45phuWxVbKvuqqq/pWOGUHB5z7iCOOaN34QufKUlDtDFmuTRsX2+DUAw884G+2VYsnNyt6NvRipp9+ei/cjO8TsA3fOOuss7xt8IruM6Kbpn7hHXydYIIJ3JRTTumvHT58uFtiiSXcyiuv7NZbbz23+eabe77uueeeaSHz8ST/v/zlL942sTcKSxPPBGi77bbvtdde3tF1t50sceTtttvOPwzhLgchWLjzJQWu0wvDAPoY+2ke/EAA4t12222+JYBAcC2B1gAkJBBvp512cjPPPLM/z/gowwxxAkJ8zqVZ4kh4xx13eExmnHHGlk3YxhgoYhiXd1SejJOCbdQ5X0D18+9//9ttsMEGrbLT6p5pppm8HWBCncblr5IasluFeDJWfOCBB/p6A9804llEnVFYsOGJtYS33nrL1yM3fcI999zjhVLqHV7B/WeffdZzCqFKwjaO71E+IFwWW5LWvB2DiHOjDK8Dy4MOOshfGmIp9ielWcQ5zZeBaHlCIkihxRNiQBDIRCXxBHnbbbf1cVdZZZW2iisC/LRp8DqL2AsxZOF6CIsD0lpOQxq6a7xWlGbR+Ii9dKewh9deJIAdT28nnXTSSJx4kLTQQgu52Wef3U033XT+4RKvyfzgBz9oa60ghLSiae1EhbDs77//vptwwgl92aPiZj2mnSHr9Z3iP/PMM44bDnUmQiPiyX6cMBVRZ1G2kR/1SCMBvoOt2MAa21ZYYYVUvIpKv4hj2MHDWmwJhTPEkuMsgiXbUo4ibIhLQ/NloMWTJ8eQ6YknnmjDi9dpOM4TyrggFZhmjaPEBQhMF/T8889vRaErTP5TTTXVEFJ88skn7sc//rE788wzW/GTNsRBIFenhbhRgSEE7KFbJ4Fy00XjONtRISq/uJZnXBphurzCQn5nnHFGeDj3tnaG3AnFXMgNjncWf/GLX/gbCA/dGPpg4WaGSEaFIursgw8+8PmEN0TqA/zGGmssL+Zh3p9++qnn1QknnBAeTtyWG0IaH0hTv9hHbwLc2AYHMGKdF8vEAmQ8qfky0OJ53333eTLRTQiDDFY//fTT4eG27SzjnSGB2xJxzr9PCqE33XTT1ikZ72GMChIhpnTNIeBVV13lbX700Ud9fGzEGcsM2CBjYZIPtvA+LIKQxjHkuqxjnjwYk7KDI1hJ2e+991631FJLSdKZ19oZMifQ4QJwAxtZ4JW0lpJanh2STXWarjdYbbPNNq342MExWvrCK8YU6b5fffXV/pw8BOQ846VxN1QSJS16E4x38oCTuqDVyMNEnvRrH2kZErFBfgglwzJsky/28iCLfcFQ1lViKeZqvjRaPKkAFnE61oBPZRBoxdG640FNGIhHN1LiheeK3r7ssss8CRm7lMAYGcSkpYf9f/zjH/0+D7J4B5VzQrDlllvOnXTSSXJpKWvyYvyJ7h5dZwJOhh04HTamDVmftkt5Kfsaa6zRKjs2kT8PO/IG7Qx500lzHRjBPRFPtrPgliaPMA7p88CGMWMJ0qP685//7A8JrxhLFJzFLoSvqnedwQF/40bMP4wYymGoh1eVFlhggSGtZMESYZXufZlYCn6aL40WTwgAuLSacDRZOCZgX3755X5capFFFvEiS8uIux8kqiKQD3ZOM800/m+Pq622mpt44om9LWLDeeed5+/AP/3pT/27gtzlaW1CNsokZSnTXmyB4CuuuKJ3KvJlqEFsTJs3Zc1yzemnn+7LinAfc8wxvoVD2RkykC5d2rx1PO0M+nyR+8JF4SBrjpUZuLHxYHGllVZy8Iq/1R577LGtRgGtehoPjMtyU+MfZDx952V+7Kui8UD55UYYYiPbDG9ofvcCS+zUfGm0eFIpOCpr6SaxzRKGt99+2z+V5Mnkyy+/nMm5w3TybkMO7Hz88cf93+cYYwwJwzatZM6zzfgUQw5Strz5Zr0O3BhC4H3BF198cQiOadLLKp6Ul6fEDE+EZZf6TJNnXBztDHHxijiO7cI91tQdx8oOvBdJffG3THgVcp/8sYNehNjGmx1V8woMJP+otcZIx6kKS82XrsWThypzzDFHq1Und4wDDjhAlzn3frevKuXO2C4sHAFaq5C/DkE7Qx1sMhvqi4DmS9fiyRdaRDDDtYlnfUlglv0XAe0MhoshkISA5kvX4sl4HKLJuqxgLc+ykB3sdLUzDDYaVvpOCGi+FCaeYauz6O8Fmnh2qlY7nwcB7Qx50rBrBgcBzZeuxZPueSicsl1kS9TEc3AIWmVJtTNUmbfl1X8IaL50JZ58H5C/NEpgm/cOEVDW4TmJk2dt4pkHNbumEwLaGTrFt/ODjYDmS1fiGQWljIGaeEahY8fqhIB2hjrZZrbUDwHNl67EU7c82d9qq618y5O1nEdIeZ0p6b/iSVBZyzMJHTuXFwHtDHnTsesGAwHNl67EM+4dz1Aow1eZ8o6D9oN48qJuL14ujqItdmT9zmZUOmUdqwtW2hnKKm836YJVGKp4sT7ML+t2+GeAJFspF3900OXLml+V8TVfChdP3V2XcdBQULMWuFfiKf9kyDr75qGHHlrJv0eicISw/M0u/AtqVLxeHANPplDgS0OMi/PB3JtvvrkXpvg8tTP0zJCYjMFGPpnIP7P4myVfaGI6jzoG6pfvQkw++eRuookmcnzW8fbbb28zlTh8FWueeebxHOAvxr30lzbjOuxovnQlnh3yKux0r8STDyPg5Fln3yR+VbNvapD5VB021008EXU+ZMt/4/k+6Ouvv+7/T13knyk0Fp32tTN0il/1eb67QF2GC19BQoDqFrAJcec7rnwOj4+QMH0wtodzcXET4P/28pFm1nzXQX8Wsm7lwx7NFxPPhFqCECy05CABd9UwIAhRs28ylXBVX6QJ7eHLQ4gmttZNPJmiGLv4/BmBj1Jwk9lll13CIlS6rZ2h0sxTZMZ/0vn4CeLDVCh8fzapK5wiydKiPP/88/7j2IijiDtTtlDnfGxHvkXAfEmhHxGXT9nx1a66lk1A03wx8RRkEtZ1n30T0yEh3wTlTh4nnpCTeEJu9hlzKpu05MdXqxB0yV/yFlsS4C/tlHaG0jLKmTDiyRQyaQI4huOHgnOaa4uII58o5PuhYgcf3IGLzIDJMeEmAhsGmTtJrgvP1Wlb88XEM0Xt9MPsm3xA+fe//70naZR44kyUgzs/nx/j6znrr7++J7d8NzQFFLmihLNv0p3jk3K05hGHsoU7yWDtDElxe3EOfJgCmyEgRPTUU08d8u40+DEGOt544/lvYPLhFTDmRsW3MWnxxQWuzbrEpcVxehUyuRz7fNEJLsIz+Idt7B9//PFtydAS5Tjd/ToHzRcTzxS1VffZN1977TU/jvTOO+94kmrxhLh8o5Svi+MscqenlcAQA/HLfDofzr5Jq0NaIXyf9LrrrktRA+VE0c5QTi75U0U8mSeKL+lzc2S8mO9vXnnllT5R6pI3WGjVU8fy9Xi+FM8nDLlR6lZeaA3jk5zXC0MF+pjsh9d32oZfcOvvf/+7j8rDQvYZyw2DiKd8xT48V6dtzRcTzxS1U8bsm/KaBkLSaenUeuCdWj4aTMCJtHjSIggnb2OWRFol5MsX7Bmf5bqogINyLs1C3Kggs2/yYIA8CaxpgfKl8Li8o9Iq8ph2hiLTLiItxO3cc89tJQW+iCdvKUh9IJQff/yxj4PYUve0ULkZgq9MWdJKJNggvSjuMcVF1HGpuyCJ2E2EkDHt3XbbrdW74IFhknjCkzoHzRcTzxS1JXfGcKCbyyCwvEoCsXgtS+JWNfvmpZde6pZffvkW2RFaEU9swkYRQLGZLt3IkSNbpE6CgPKkmXmTOBofSZf3gbGJOOKA2IQdHGdsrBdBO0MvbOiUJziFQTDjY9SE8MYj3EuaeytMq6xtekDM3kCPTeqbvBh+oL7juu08RKxz0Hwx8UxRW0JKLQ7dzL5ZRMsTx+J9Oeb2oTWy7LLL+tYGBOX9uaWXXrrtNRGK2svZN5lKQ8QApxchkNdWUlRFoVG0MxSaeJeJITrcmHkIKJiRpGD2r3/9qy0H8OTmxLw/oaC2RVI7jE/SQk27pKkneM00McyLhB3YLtOlMEQDN7UfMa7Lcf6RWOeg+WLimaK24sSzDrNv4mThIjN/4mQQGQLjHJQB8svsmzK+VNXsm9jD3Ezi2DgVxxB/7OxF0M7QCxvi8qROwWu++eZrYUZcEU/ek+VGyAR4jEeCIQLEPFMS2KfrHxeYypn4cQvDQeHCuHlSwGb+JCOzBVDHHMNm6p0HQtiEvRKIw1zxEkeO13Gt+WLimVBLVCyVHoonZBABgLxRs29CDloBEi8hi0JPkR/2QVDIiENRBpklEfHUsyRCXFoJZQZs4F8l2CVdSuxk9kPy5nwvgnaGXtgQlyd1SYssfMGc8Uum+uXVOc7ffffdHtMRI0a4UaNG+W1p1XGeMU9wriJQh3CeBe6FCy/PYw/L6quv7n1G7KKrzqtMoaBWYW+ePDRfTDwTUKRCIUGW2TcZJGfK16r/MQF5o2zF+Xgiy1/mEC+e3MosibQ4OAapyw44y7rrruvHZ+WfW7xa1atWJ+XVzlA2BlnTp2XIQzZaf7T64CGCKpiBKbOIwjdmvGRmzAknnLA1qyovrlcV4BlcilpCYaTFzJDS5ptv7m8M2223nbe/Cg52i4Xmi4lnAqJUKARlDWFZyxJe1uvZN8UWsU1sZk1AWGkly+ybxOvFLInYwRACT4Xzzr4pZS1irZ2hiDSLToN64r1NPrDDgxgwDAN1zMyYUvf8y0z2w3hlb0v+ceswf+LIUNJjjz02pExh3Dpta76YeNapdsyWShHQzlBp5pZZ3yGg+WLi2XdVaAYXhYB2hqLStXSaiYDmi4lnM+vZSpUCAe0MKS6xKAOMgOaLiecAk2HQi66dYdDxsPInI6D5YuKZjJedbTAC2hkaXFQrWgEIaL6YeBYAqiXRnwhoZ+jPUpjVVSGg+WLiWRXylk/tENDOUDsDzaBaIaD5YuJZq+oxY6pEQDtDlXlbXv2HgOaLiWf/1aFZXBAC2hkKStaSaSgCmi8mng2taCtWZwS0M3S+wmIMMgKaLyaeg8yGAS+7doYBh8OK3wEBzRcTzw6A2enmIqCdobkltZIVgYDmi4lnEahaGn2JgHaGviyEGV0ZApovJp6VQW8Z1Q0B7Qx1s8/sqRcCmi8mnvWqH7OmQgS0M1SYtWXVhwhovph49mElmsnFIKCdoZhULZWmIqD5YuLZ1Jq2cnVEQDtDxwsswkAjoPli4jnQdBjswmtnGGw0rPSdENB8MfHshJidbywC2hkaW1ArWCEIaL6YeBYCqyXSjwhoZ+jHMpjN1SGg+dImnmP9YJir64LhthgGxgHjQC85EEp1SzzDg7ZtCBgChoAhkIyAiWcyPnbWEDAEDIFIBEw8I2Gxg4aAIWAIJCPw/wGND6VR4zq7sgAAAABJRU5ErkJggg==[/img][br][size=150]While one partner listens, the other partner should:[/size][list][*]Choose a pair of equations from column A. Explain why, if [math]x[/math] is a number that makes the first equation true, then it also makes the second equation true. [/*][*]Choose a pair of equations from column B. Explain why the second equation is no longer true for a value of [math]x[/math] that makes the first equation true.[/*][/list]Then, switch roles until you run out of time or you run out of pairs of equations.
Noah is having trouble solving two equations.
[size=150]In each case, he took steps that he thought were acceptable but ended up with statements that are clearly not true. [br][br]1. [br][math]\begin {align} x + 6 &= 4x + 1 - 3x &\quad& \text{original equation}\\ x + 6 &= 4x - 3x + 1 &\quad& \text{apply the commutative property}\\ x + 6 &= x + 1 &\quad& \text{combine like terms}\\ 6 &= 1 &\quad& \text{subtract }x \text{ from each side} \end {align}[/math][br][br]2. [br][/size][math]\begin {align} 2(5 + x) -1 &= 3x + 9 &\quad& \text {original equation}\\ 10 + 2x -1 &= 3x + 9 &\quad& \text{apply the distributive property}\\ 2x -1 &= 3x - 1 &\quad& \text{subtract 10 from each side}\\ 2x &= 3x &\quad& \text{add 1 to each side}\\ 2 &= 3 &\quad& \text{divide each side by } x \end {align}[/math][br][br]Analyze Noah’s work on each equation and the moves he made. Were they acceptable moves?
Why do you think he ended up with a false equation?[br]Discuss your observations with your group and be prepared to share your conclusions. If you get stuck, consider solving each equation.
We can’t divide the number 100 by zero because dividing by zero is undefined.
Instead, try dividing 100 by 10, then 1, then 0.1, then 0.01. What happens as you divide by smaller numbers?[br]
Now try dividing the number -100 by 10, by 1, by 0.1, 0.01. What is the same and what is different?[br]
In middle school, you used tape diagrams to represent division.
This tape diagram shows that [math]6\div2=3[/math].[br][br][img]data:image/png;base64,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[/img][br][br]Draw a tape diagram that shows why [math]6\div\frac{1}{2}=12[/math].
Try to draw a tape diagram that represents [math]6\div0[/math]. Explain why this is so difficult.[br]
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Information: IM Alg1.2.7 Lesson: Explaining Steps for Rewriting Equations