Question

5x+2-3(x+2) =-2(x+1)+5(x-2)

Answer 1

Answer:

$5x+2-3\left(x+2\right)=-2\left(x+1\right)+5\left(x-2\right)\quad :\quad x=8$

Step-by-step explanation:

$5x+2-3\left(x+2\right)=-2\left(x+1\right)+5\left(x-2\right)$

$\mathrm{Expand\:}5x+2-3\left(x+2\right)$

$5x+2-3\left(x+2\right)$

$\mathrm{Expand}\:-3\left(x+2\right)$

$\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac$

$a=-3,\:b=x,\:c=2$

$=-3x+\left(-3\right)\cdot \:2$

$\mathrm{Apply\:minus-plus\:rules}$

$+\left(-a\right)=-a$

$=-3x-3\cdot \:2$

$\mathrm{Multiply\:the\:numbers:}\:3\cdot \:2=6$

$=-3x-6$

$=5x+2-3x-6$

$\mathrm{Simplify}\:5x+2-3x-6$

$\mathrm{Group\:like\:terms}$

$=5x-3x+2-6$

$\mathrm{Add\:similar\:elements:}\:5x-3x=2x$

$=2x+2-6$

$\mathrm{Add/Subtract\:the\:numbers:}\:2-6=-4$

$=2x-4$

$\mathrm{Expand\:}-2\left(x+1\right)+5\left(x-2\right)$

$-2\left(x+1\right)+5\left(x-2\right)$

$\mathrm{Expand}\:-2\left(x+1\right)$

$\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac$

$a=-2,\:b=x,\:c=1$

$=-2x+\left(-2\right)\cdot \:1$

$\mathrm{Apply\:minus-plus\:rules}$

$+\left(-a\right)=-a$

$=-2x-2\cdot \:1$

$\mathrm{Multiply\:the\:numbers:}\:2\cdot \:1=2$

$=-2x-2$

$=-2x-2+5\left(x-2\right)$

$\mathrm{Expand}\:5\left(x-2\right)$

$\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac$

$a=5,\:b=x,\:c=2$

$=5x-5\cdot \:2$

$\mathrm{Multiply\:the\:numbers:}\:5\cdot \:2=10$

$=5x-10$

$=-2x-2+5x-10$

$\mathrm{Simplify}\:-2x-2+5x-10$

$\mathrm{Group\:like\:terms}$

$=-2x+5x-2-10$

$\mathrm{Add\:similar\:elements:}\:-2x+5x=3x$

$=3x-2-10$

$\mathrm{Subtract\:the\:numbers:}\:-2-10=-12$

$=3x-12$

$2x-4=3x-12$

$\mathrm{Add\:}4\mathrm{\:to\:both\:sides}$

$2x-4+4=3x-12+4$

$Simplify$

$2x=3x-8$

$\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}$

$2x-3x=3x-8-3x$

$\mathrm{Simplify}$

$-x=-8$

$\mathrm{Divide\:both\:sides\:by\:}-1$

$\dfrac{-x}{-1}=\dfrac{-8}{-1}$

$\mathrm{Simplify}$

$x=8$