Answer:
[tex]x=-14[/tex]
Step-by-step explanation:
[tex]\frac{x+7-8x}{3}=-\frac{5x}{2}\\\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c\\\left(x+7-8x\right)\cdot \:2=-3\cdot \:5x\\Simplify\\2\left(-7x+7\right)=-15x\\\mathrm{Expand\:}2\left(-7x+7\right):\quad -14x+14\\2\left(-7x+7\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=2,\:b=-7x,\:c=7\\=2\left(-7x\right)+2\cdot \:7\\\mathrm{Apply\:minus-plus\:rules}\\+\left(-a\right)=-a\\=-2\cdot \:7x+2\cdot \:7[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:7=14\\=-14x+14\\-14x+14=-15x\\\mathrm{Subtract\:}14\mathrm{\:from\:both\:sides}\\-14x+14-14=-15x-14\\\mathrm{Simplify}\\-14x=-15x-14\\\mathrm{Add\:}15x\mathrm{\:to\:both\:sides}\\-14x+15x=-15x-14+15x\\\mathrm{Simplify}\\x=-14[/tex]
