IM 8.4.6 Lesson: Strategic Solving

The triangle and the square have equal perimeters.
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[/img][br]Find the value of [math]x[/math].
What is the perimeter of each of the figures?
Triangle:[br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGQAAAD0CAYAAABthIMXAAAbqUlEQVR4Ae2dCdRXwxvH87dlC1mTKBKFiIhU9lJoEREllaKyRipRSChRylpKCCmOJCokS8jaZpclZMlO9mX+5zPnPO+Z93Z/+72z5H3O+Z17f3PvnTvzfGfmzjPPMpVUBXnFgUpelaaiMCpIQH7//Xf13XffqX///XeNgzBIQGbPnq26deumfvjhhwpAfOBAv3791FprraUWL17sQ3ESLUNwPYRh6uSTT1aVKlVSTz75ZKLM8CGz4AD5559/1MEHH6wBufvuu33gYaJlCA6Qn376Se26664akGHDhiXKDB8yCw6QTz75RG211VYakF69evnAw0TLEBwgr7/+ulp33XXV//73P9W2bVvFELYmUXCAzJgxQ6299tpq++23V/vvv7/65Zdf1iQ8whMMR48erTbbbDPVunVrtcMOO6gvv/yyAhCXHDj77LNVrVq11GWXXaaqVKmili5d6rI4ib87uCGrXbt2at9991XTpk1T66+/vnriiScyMiXEpZWgAIHBDRo0UICycOFCtd5666lJkyZlBCTEC0EB8v3336tq1aqpPn36qJUrV6qqVauqyy+/XPM9xN4Q12CCAuSDDz5QG2+8sRo+fLhixRcBsXv37mX1WhNACQqQF154QU957733Xg1CkyZNVIsWLdYoWSQoQB544AEtoT/77LMaEBYZ69evHyuLhNpbggLkuuuuU5UrV1bvvvuuBmTAgAFq66231t8TGbdCBULKHxQg5513ntpmm23KALj55pvVBhtsoN566y2pT/DHoABp3769qlevnvrrr78046dPn66nvnPnzg0eCKlAMID8+eefqlGjRqply5ZluvSXX35ZAzJ58mSpT9m1soTAToIBBKOGGjVqqLPOOquMxR9//LGWRYYOHVqWFvpJMIAsW7ZMbbLJJmrkyJFlPMfIISqLlF0M9CQYQJ5//nmtB2ENS4hvCbLIEUccIUkVQ1YZJ1I+QQbB0mTBggXl3tSxY0e1xx57xMoi5W4M5E8wPQQZZMMNN1Qsn5g0cOBArdL95ptvzORgz4MBBBmEj7owXgTA2267TQuLb7/9drAgmAUPBhBkEJbemf6aJCrdNcVGKwhAWNk94IADtNpWeoaA8uqrr+oFx7vuukuSgj4GAQgyCPpzUwYRrn/22Wd6SX5NkUWCAIQP+aabbqquvfZawaHs+OOPP6ratWtr4+uyxIBPggAEPQj6c9GDmPxGFjnooIPUYYcdZiYHex4EIA8++KAWCkUPEuX2iSeeqHbbbTf166+/Ri8F9z8IQG644QZt8iN6kCiXkUXQr68JNlpBAHL++edrGeSrr76KYqH/I4tgzfjGG29ULJ3EcijBRKa5xx13nGrYsKE2bIjLeubMmVq1+/jjj8ddDirN+x5iyiCZOIssss4666iJEydmuiWYdO8B+fbbb7XpKLZYmQhZhKV5sdHivqgAmelZ39K9B+S9997TH/Trr78+I+9WrVql6tSpozp37lzunhBB8QKQbIxjqosMMnXq1HLMNv/gI3LIIYdo3Ujo/iJeAGIyN3oOEDjozJ8/P3qp3P9OnTpp7eHPP/9cLj20P94Dgh4E89H3338/K28vueQSteWWW6pPP/00632+X/QKkLih65xzzlE77rijtsWKXjf/T5gwQQ9tWMVD5jXfQTDL5xUgZsFgKD9cD/bbbz/122+/mZfLnXMf+hD8Dh977LFgwaBSXgESbdUoowCjTZs2msnR6yYqSOmYmd56661mcnDnXgES5R4yCGpbhq1cxLLKFltsoQYNGlTRQ3Ixq9jr2GJh2IAMEu0d5n/OkehZ8Y3KIsW+29VzXveQOFssEwiTaX///bc6/PDDtTyS6R7zfl/PvQYEGQQ/wueee07zL47RZtppp52mZRG0iKGSt4DAaIYq1qgYukzGZ2L24MGDtY0W4TdCJW8BgaH4pGPc8PXXX+fFX1Z7WWYRWSSvhzy7yWtAiNaQTQ8S5SWR5lBUcQyVvAUEGYQAAYCSz3DFPYsWLdKzsnHjxuln8nnON+C8BQSfdGQQhq1sZDIdvQgub6xrhUpeAWIyF1ss/AdNf5BcTEYvUrdu3aBlEa8AMRmODIL7gekPYl6PO0cWad68uQ4BGKpexBtAzN4Bs++//36tJxcZJA6AuLSuXbtqWYRQgCGSN4BEmTdixAi9WBj1B4neZ/4HVMI2EQIwVL2IN4DATLOXEE+xevXqigXGQgi9yEYbbaQIBRgieQOIyTyAadWqlZZBov4g5n1x53PmzNEq31mzZsVd9j7NS0BYud1rr710kMsoB81eFL3Gf1MWibvue5qXgOC2tt122+WlB4kymG8H8U8uvfTS6KUg/nsJCLZYaP+y2WJl4i6yCHoRVn5DJC8BwRaL2O6FyCDCfNGL4C8SoiziHJC4bwIx3bHVxVGnGOrSpYvuJSHG9HUOSBzDr7nmGj11LUQGkXwAGFkkVBstLwHp3bu3lkGK1fwhi7AOxowrNPIOEMZ9QjARRrxQGUSYj58I3yBkktDIO0D++OMPHUcRJ51iiCGLnkEPGT9+fDFZOH3GO0Cwr0IG6du3b9GMEVkEG63QyDtAiJ+IcfWYMWOK5iWyCHG0sIgPjbwD5JlnntFT3oceeqggXprTZ75D2GixNVJo5B0gBAfAFuull14qiZfIIkR4yGakXdILUnrYG0CkhV999dV6f5APP/ywpCqjV998883VF198UVI+th/2BhCpuNhiFSuDSD7MsOhpUVlEgJf7fDt6BQjMwuyHUEyFyCBRJvMffQg6+dD0Il4Bgh5kn332Uccff3zJDXfJkiW6h9xyyy0l52UzA68AYU8Q3NcuuOCCknmwYsUKrVu/6KKLVssr2qNWu8FhgjeAwKR33nlHG1cTbKZUYqUXWeSkk04qNSurz3sDCLUuVgbJxDF815s2barQkYRCXgEiMggx3ZMgtIY77bSTQnI3qWLIMrmR5RwZBNkBf5B8SZgrR/O5IUOG6NCAIfmLeNNDYKjsUYihdRKEvwiyyGuvvZZEdlby8AYQanvMMceoxo0bZ4yLlY0jcT2EPQ6RRR599NGyR+PuK7vowYk3gCCD4A9SigwSZfabb76pHXhC8l33BhDc1thwmHB+hVIUCHmedSxiMV588cWS5P3RG0CQQYjNO2rUKM20TEwuhKNEKWWLJHZQCIW8AQS3Az7Api1WPqDIPdEjAJB25JFHallE9q2S+3wFyBtA8AchLhaOOknS6aefrvUi0dVjX4HxBhDCiLNPOmakxVIck6+88kqdbyiyiBeAwEhkEBYWZX+QYkGJPocVJL7rr7zySvSSl/+9AATOHHvssVoPghlQkkQcLcxSie0LxfWiJN9Xal5eAAIIbNbCpi1JkDCdI7IINlqhyCJeAELMdvzLieGeNDEEIt+UYueVdJmy5bcaINK6eAg1KsIVBgcYsJnL2OZ92V6QzzX2jyIuFnvbJk3IImghi+l9mBMhsFJ/FF5JD6dxdV0NEG6C8RgH3Hjjjapfv37akwktHtsKiROmACLHuMzzTZs3b56OlyjjfL7P5XMf5Tv66KMLWiPjGUC48847FRrHc889V68gjB07Vn300Uc5Xys8kWPOB4wbYgFhiyG2F6JVXXjhhdq8v2fPnnqtCW2e2VOMvIo6pdAAjQySxqos+ePRu/POO5c1pmwF5X6ESFQBxHokvCDuDewSd+CBB+pjmj7wGhBBUo4IUaNHj9ZRdeiqbHGKjoIN5VGLmvt0sCgoz5kVJT1f4K644gqtB2FvW5Pi8jWv53NOHvi8I+Pkiv0r7wMQegcB1JYvX67gB/bClJO1MdOIj2E9bhWA4U3S8ymn3BPbQyhY1PuINFoyYz0zF4gxlqWORx55RPLTR0xvsIsCyFxEvt26ddMtOJ/7c+UXd33KlCnaZ7GQVQC+PdTPJHowyztm2HPc75B15PtCfbiP4T7awMy8Mp3HApLpZqJM4+FKq4F4Od2Z/WglyNiLL76o147wgs0n7Dd5sJcteUiPIi1Jgmkwku1bSyFkGhqkuWciebL1K99cyg0IJ5xwgg6Aw+hSKK0GSCZmMMvCeJmVU9NeFv0300r2iaIwfHf4ZdqeKFpAWhbDYHRFNlM5os/n85+yEN2BYdikuHfEpfEMPeaMM87QjkTCaO79/PPP1d57761QFzPhYfJD46IRZMrLLEP0vNw3JHpR/tPS2ZuDloBlCCQv41uB2T8Wh3z4aO2FfJz5HqFH79+/v7wu8SP2XqYsImXP90UMXZMnT9ZL+bjLRYkJAAGf+cY0atRIYblf6Dskz9V6iFyQIy2D8ZC5PHs9RU08eTHbn8JU7sGNLK4wkiZHyR8LQ9aa0pBB5B18D9FGFiOLkAf1Y2s+Gk2cvh85qlatWtrChWh2UR5JOfI5VooyyHyIoYklB/TcOPHLdM98htYDUDAVG6joZMDMz3yOdP7jD0jM9jRkEHk3ZURfz7SVHp0vUT708YceeqiWQzJFGOKbsu222+rvaz5ySrb3r9ZDKAQ/wGCm1KxZM8XHPNMHmoCTfFtOOeUU/S2I7nee7eVcu/322/XiX9rRe5BFsNFCxhKiniaZ/zknsD+OPwiGmcCghwM230BkHabLpdBqgJAZrZyxkm46bNgwvSROy+IHUDK/ZjMuWg9CJN2WHsK5XDcLZlbWTCfWLsNdmvoK3j18+HC9dVKuqSj3MtujoQEGQPIMkw+pvwxJlJnQ5m3btlVLly5VPXr00A24lOl7LCCoU5n5EDMXhqE8okL8cOqnsCiSKAitA4GLirC0ULNmzTI5xWR8pvNTTz1Va/Si1oWZ7i82/Z577tHDKtPyXAQANMYqVaroiQr1p95Sfz7wrPExicF1ghkVxBIQwdOYcRZLsYDAcNZ/MMmhBTAcMZPiSNfkw4UwyJanprBFRTp06KCwhwIgftmIsZ1WyDeKcyjXM9nyy3SNPJ9++mkNSD7MwuAC/QwzRxoM9ZYf9Wc2hbTOygVAi/zEyHLmmWfqSVCx9YgFBJkDDRsyBi/mJ+d8Iwh5Qa9YvHhxGSNhBkxlTM02/JgFpVcQRdS0UDevZ2JwMekMqVi1RGWRuLz4XjIcS52FB3JkrxLqCI+YhZrEEhPvKrYesYCYL0jzHKGKPT/S0INEy40swhCMXqRYZhX7XLQs2f47BYQehjYvTRlEKs9khLDlxUaIkHzSPjoFRGQQppdpE61b9PYyC7TR4gutl1NAJk2aVLbLc6EFL+Z+kUVKmZYW895CnnEKCAty6Bcy+ZIn0YLJQ/Jh6opepFQf+EIYXOi9TgEh2gJ72GZbbim0Qtnuv++++/SqgM82Ws4AYe5OXET8AEUGgZnSmrMxtthryCLoRaZPn15sFqk/5wwQkUEQvGwR8gEKJlYUfCVngKDkIS6izfi6yCKsymK44Ss5A0RkkLiob2kNWywOYiEpskha7ykFbGeAIHswntuQQYRBfKuQRVBWiSwi13w5OgGElokexEXkUGQRtlLyVRaxCog5RLCsbzu2Lu/HRosPu6+yiFVAzGGBKAvEaI96Npn3pHFOtAhcpfPRi6Tx/lx5OgGEsRw9CKpfUwahsGYvylX4Qq+TN8ok9jo0jd0KzSfN+50AgrHE7rvv7iRqKMonbLQK2f0tTQCieTsBROLquthvEH8RZJFc+yNGGWXrvxNA2KvWVeRpjBXYvQf1rI+UOiDmN0HO0dkjg5gxSNJmjrybI/tbISD6KIukDkgcozExwrDOxa7OAIIhAqalpo1WXDldpDkBBDthdOnsXeuC0IuwT3spPvFpldsJIPiDIIPYkJZlqBIG8p8pL+ar8+fPl2RvjtYBQQ9C/BEsHsUC0DY32EoJWQRHHt/IOiBoB/fcc09tgBdtvbaYg10ZOzBgkegbWQcEWyybe57Hgc5QWew+iWkDaB0Q/BPZozBOD5J2ZSV/lmvwZcE2OQ4wuc/F0Tog2GLhAm1TDxLHWMDA6wmllU+UOiDRFogMwvJ32v4guZiM5TqmpUlHH8r13lzXUwdECiDA4LWLDJLJAUbuT/uIR1ip8bnSKGPqgAgQUnjRg4h7nKTbPuLOzNTXdKewXYa496UOiPlSwMEWCxnE9ToSCiriaJkxHs2yujq3Cgi+FOhBcH5xTfi34C+C/6RPZBUQfNKJBOFDHF2c/AkpSHAZoejwKuk2j1YBYY9CVnl9iO7Gsg3buzL9FTXyfw6QuXPn6g+pTT1IptYN89u1a6dlEQkck+lem+lWewj+IPQQ/PdsUaZWTzr+5+hFfJJFrAAiTEEPwtw/m1OoLaB4j8QKzhVHy2aZrABChQAFGYRoB5miQtisOO8imjY91idZxAoggMGHEzusOFss20DI+7DRApBS42hJfkkcrQBCQVnyZppJLHZfCL0I5qyEV/KFrAFClAf02ERB8IVoJAyhGD1ESb570fS0/1sDhKBm6LGJ2+gDwXCWbwjZhIuC66Uc4Yk1QB5++GFt5GzGK5RC2DpGWz3/ideC4RzLOtHrtsplvscaIGPGjNGaQoloahbC5fmAAQNUtWrVdORuyuEaFGuAEByS0EVmzF+XQMi7CV/It41lHddgUCZrgBDxB1ssWabwofKUgaGUZXgJ7ilAuTpaAQRbLKJ1Yo8lC3lU2AdQCMEEIMS98oGsAIJ2kKidWCz6Rri2EWIwKou4aixWAKHSrGH5JINIw0AvgixCkGRXIEhZOFoBhEhsDAvESPeNkD+Im0hIw/8MIMQWwaCA4Jo+ErHakUVkwuGyjKn3EFodMgi2tBIP3oeWaDKdTWswb/XBXyR1QKg4Mgh+faYiyCdQ2KQGFztpMCZYts9TBwTGszyBxbsPQ0KUwZSP4Pl84wjf5JpSBwRjAoISt2zZUtfVp54hzGfSwTeOoAKuKXVA2E1Alrh9BAMAUA0wLWebVteUOiDIINjyXnXVVa7rmvH9NBoC9Xft2jXjPbYupA4I8Q1xgSZeuo9Er0UWYWmHzWhc9+JUADErRYx4xmcW7yRdjj4BRJx7zFwJuOySUgFEKgTjb7rpJh1bhOVtn4mwf5i5yuZmlNVFw0kVECqF0FW9evWMsXl9AQm9CEMrCjQXQAgfUgWEiqEHYRcz10OBVDjuSDlleeepp56Ku8VaWqqAiAzCpi+mHsRa7Qp4EXoRApu5NsJIDRBaHdHimE7GmdkUwKvUb6WsmLey3uZaFkkNELjIjmUof9jHyneKU6IBlG1KFRCGARbtTD2IVFKOtiuc6X2omdGLRNXMme5PKz1xQITRHJFBWLTDLyQEQi/Cbqa2NgeI40nigJgvYeccTGzYsykEYjN716ZKqQFCD8EIjZgixDcJgdixlCgTLhtQaoAAANvK1a9fX8sgMpT5DAyudtgfuzR3TQwQYbgckUHwBWnevLlTybeQBkC4D/xF7rjjjkIeS/TexACJloppJHqQnj17lrskgJVLdPjHLA8hB12bK6UGyPLly4ORQWgPAEMjql27turevbuzJpIYIGZLozbIIHR/UwZxVss8X4ws0qRJE6d6kcQAidYZGYQPZLbFuiiI0Txc/GcxFFnElWNqooCYDEYGIS6W73oQQDfL3b9/f22y5GqqniggZotGD4IjTNQfxKy8eb8P55SNsB80JPZHd0GpASK2WC6XIYphKLIIwiFbkLugVADBaABbrDgZxOceAgCE/WBBlDAgLigVQOgVNWvWVD169Cirk+9ASEEJPYgsMnToUEmyekwcEBiPgIWyx1WlSuEgSjVkEQRaF40oMUDMwtPtGYddLkEUAopZdpZ8mjVrplq0aOFE7ZwYICYDMBhAPx2KHsQsO+B06tRJG4e7kEVSAUR80tl7NkRCbeDKdClxQGhhBCnGHyQqg/gIjjlcSflEFnER5CBxQKgUofNYfvDZFkuYH3ecOXOmNn91MeQmDggfRfFJj2t9cQzwLY1AOUjrLiYliQOCaT9xsUwZxDeG5yoPqgNcKFxM2xMHROJihWCLlQkY4mjVqVPHSaNKHBAJ4R2SHiQKjMgiLP3YpsQBwYESGSSbHsR2JYt5X8eOHbW/CHG0bFJigMgHfOzYsdo4zsct6bIxVsrPPZyjF8GEyfbUPTFApLI4vmBsZjq+yDWfj4BggiKORiLcmtfSrEfigLRv395bn/RCGDljxgzd0+fNm1fusbSBSRQQ9nNiX6c2bdqUq0SIfxYtWqT1IrZlkcQAoeUwTLGvU+fOnbW/BVNg33/IHPwop3kk2nWVKlUU4dFtUmKAUGgqhB6EjVLq1aun6tat6/2PsIP8zPJyjhzCbNEUcNMeruBhooCwXD1ixAhtZM2mLT78Bg0apAYOHLhaWeLS4sprW7eeKCC0IEBB68YPiVfOXR6xSDTLYp7nKpftfQ4TB8TmeJvvu4odaop9Lt9yxd2XKCC8wEUl4ioWalrigPgISpKNJMm84hpNyYBECxj9H/dSX9J8LGvJgPjCXFvlSBvE/wQgzJQQ/IjdZXvWVGhD8QqQbK2Pa9muZ6o4NmL4OjZt2lTvFYLNMTG8fCVvACmG2SZTzeflnEgSxONFt8E+7uzhTpCyBg0aWF9WN8ua7dwZIIT4RtcA84SBDCcsvyRlMc/CIMYKGC0QEZWfRP0BHB/JKiDCeBiBipeVYYmVC7P69OmjTYhWrlxZxivzmbLEHCfyzMSJE/V6FGploalTp+q0BQsWSJJXR6uAmDVftmyZjiY9ZMgQnTxq1Ci9Ujxr1iyFr1+xJGDwPEbfDRs21N8PXOzmzJmjTZR69erlrc2YM0DwIenbt69eZZ0yZYrezmLChAmxwZaJtQVIHOUH4+WcI/9NMACEdIzeMOmpUaOGDuGHZbvNrV8LbVjWATGZhqkme9HCLMyG4gwKsAAZOXKk3iWUPRBxWebIj6Vx9iTp3bu3WrFixWp1J//GjRurDh06qNmzZ6tx48bpjzyetj5tt2oW3Dog5stxna5ataoOkrlw4ULzUllrp2ewLRExEdFzmz8cS/k/fvz41QLpA3yXLl20roOJAsAyWWB3T/Q1xKP3kZwBApNwe6OFY92RbbMXbIRZ1l+1alXZD+aa/82eB6OZsaEga9WqVRm4ko7yiXQfyQkg6CDQuxMLBfdjvJXYEilpV+TWrVtrT2DTJIkZV+XKldXgwYN9xCNZjWE+NaRlM+bvsssu+uNKyyYYPlEf2DYiKSJfmE8vQRDE54NhCvXsUUcd5c0W4tH6Wu8hCIPsY45qlJkWhAzCt2DatGnlhpdoYXP9l2FLjnw3lixZojf8ohfSEIiJlXRPzFWuQq5bB4SPNCpVQDCJ70HcLMu8p5BzAYWpL+9jZYAfPZRrcr2QPG3cax0QG5UK+R1WAUmiVUbzyPU/NHCsAQLjoswrlFnFPl/sc4WWL4n7rQGSRGH/C3lUAOIZyhWAVADiGQc8K05FD6kAxDMOeFacih5SAYhnHPCsOBU9pAIQzzjgWXEqekgFIJ5xwLPi/B+kC1hp8mWFnwAAAABJRU5ErkJggg==[/img]
Square:[br][img]data:image/png;base64,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[/img]
Without solving, identify whether these equations have a solution that is positive, negative, or zero.
[math]\frac{x}{6}=\frac{3x}{4}[/math]
[math]7x=3.25[/math]
[math]7x=32.5[/math]
[math]3x+11=11[/math]
[math]9-4x=4[/math]
[math]-8+5x=-20[/math]
[math]-\frac{1}{2}(-8+5x)=-20[/math]
Here are a lot of equations:
Without solving, identify 3 equations that you think would be least difficult to solve.[br][br][table][tr][td]A. [math]-\frac{5}{6}(8+5b)=75+\frac{5}{3}b[/math][/td][td]F. [math]3(c-1)+2(3c+1)=-(3c+1)[/math][/td][/tr][tr][td]B. [math]-\frac{1}{2}(t+3)-10=-6.5[/math][/td][td]G. [math]\frac{4m-3}{4}=-\frac{9+4m}{8}[/math][/td][/tr][tr][td]C. [math]\frac{10-v}{4}=2(v+17)[/math][/td][td]H. [math]p-5(p+4)=p-(8-p)[/math][/td][/tr][tr][td]D. [math]2(4k+3)-13=2(18-k)-13[/math][/td][td]I. [math]2(2q+1.5)=18-q[/math][/td][/tr][tr][td]E. [math]\frac{n}{7}-12=5n+5[/math][/td][td]J. [math]2r+49=-8(-r-5)[/math][/td][/tr][/table][br][br]Explain your reasoning.
Choose 3 equations to solve. At least one should be from your "least difficult" list and one should be from your "most difficult" list.
Equation 1:[br][size=85](least difficult)[/size]
Mai gave half of her brownies, and then half a brownie more, to Kiran. Then she gave half of what was left, and half a brownie more, to Tyler. That left her with one remaining brownie. How many brownies did she have to start with?
Equation 2:
Equation 3:[br][size=85](most difficult)[/size]

IM 8.4.6 Practice: Strategic Solving

Solve each of these equations. Explain or show your reasoning.
[math]2b+8-5b+3=-13+8b-5[/math]
[math]2c-3=2(6-c)+7c[/math]
[math]2x+7-5x+8=3(5+6x)-12x[/math]
Solve each equation and check your solution.
[math]-3w-4=w+3[/math]
[math]3(3-3x)=2(x+3)-30[/math]
[math]\frac{1}{3}(z+4)-6=\frac{2}{3}(5-z)[/math]
[size=150][size=100]Elena said the equation [math]9x+15=3x+15[/math] has no solutions because [math]9x[/math] is greater than [math]3x[/math]. Do you agree with Elena? Explain your reasoning.[/size][/size]
The table gives some sample data for two quantities, x and y, that are in a proportional relationship. Complete the table.
Write an equation that represents the relationship between [math]x[/math] and [math]y[/math] shown in the table.
Graph the relationship. Use a scale for the axes that shows all the points in the table.

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