Question

Solve & Justify: 7(x + 3) + 9 = 5(x - 2) - 3x

Answer 1

x = -8

Explanation:

`7(x + 3) + 9 = 5(x - 2) - 3x\\\\\mathrm{Expand\:}7\left(x+3\right)+9:\quad 7x+30\\\\\mathrm{Expand\:}5\left(x-2\right)-3x:\quad 2x-10\\7x+30=2x-10\\\\\mathrm{Subtract\:}30\mathrm{\:from\:both\:sides}\\7x+30-30=2x-10-30\\\\Simplify\\7x=2x-40\\\\\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}\\7x-2x=2x-40-2x\\\\Simplify\\5x =-40\\\\Divide both sides by 5\\(5x)/(5)=(-40)/(5)\\\\Simplify\\x = -8`

Justification

`7(x + 3) + 9 = 5(x - 2) - 3x\\x=-8\\\\7(-8+3)+9=5(-8-2)-3(-8)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(-8+3\right)\::\quad -5\\=7\left(-5\right)+9\\\\=-35+9\\\\=-26\\\\5\left(-8-2\right)-3\left(-8\right)\\\\Follow\:the\:PEMDAS\:order\:of\:operations\\\\\mathrm{Calculate\:within\:parentheses}\:\left(-8-2\right)\::\quad -10\\=5\left(-10\right)-3\left(-8\right)\\\\=-50-3\left(-8\right)\\\\=-50-\left(-24\right)\\\\=-26\\`

`-26 =-26`