Question

Solve for x. a²x+(a-8)=(a+8)x

Answer 1

$a^2x+(a-8)=(a+8)x\\\\(a+8)x=a^2x+(a-8)\ \ \ \ |subtract\ a^2x\ from\ both\ sides\\\\(a+8)x-a^2x=a-8\\\\(a+8-a^2)x=a-8\ \ \ \ |divide\ both\ sides\ by\ (a+8-a^2)\\\\\huge\boxed{x=\frac{a-8}{a+8-a^2}}\to\huge\boxed{x=\frac{8-x}{a^2-a-8}}$

Answer 2

Solve for x.

a2x+a−8=(a+8)(x)

 Add -8x to both sides.

a^2x+a−8+−8x=ax+8x+−8x

a^2x+a−8x−8=ax

Add -ax to both sides.

a^2x+a−8x−8+−ax=ax+−ax

a^2x−ax+a−8x−8=0

Add 8 to both sides.

a^2x−ax+a−8x−8+8=0+8

a^2x−ax+a−8x=8

Add -a to both sides.

a^2x−ax+a−8x+−a=8+−a

a^2x−ax−8x=−a+8

Factor out variable x.

x(a^2−a−8)=−a+8

Divide both sides by a^2-a-8.

x(a^2−a−8) / a^2−a−8 = −a+8 / a^2−a−8

$\sf x = \dfrac{-a+8}{a^2-a-8}$