Answer
$x=8$ and $x=−4$
Work Step by Step
The given equation is
$\Rightarrow |20+2x|=|4x+4|$
Write related linear equations.
$\Rightarrow 20+2x=4x+4$ or $20+2x=−(4x+4)$
Solve the first equation.
$\Rightarrow 20+2x=4x+4$
Add $-4-2x$ to each side.
$\Rightarrow 20+2x-4-2x=4x+4-4-2x$
Simplify.
$\Rightarrow 16=2x$
Divide each side by $2$.
$\Rightarrow \frac{16}{2}=\frac{2x}{2}$
Simplify.
$\Rightarrow 8=x$
Solve the second equation.
$\Rightarrow 20+2x=-(4x+4)$
Clear the parentheses.
$\Rightarrow 20+2x=-4x-4$
Add $-20+4x$ to each side.
$\Rightarrow 20+2x-20+4x=-4x-4-20+4x$
Simplify.
$\Rightarrow 6x=-24$
Divide each side by $6$.
$\Rightarrow \frac{6x}{6}=\frac{-24}{6}$
Simplify.
$\Rightarrow x=-4$
Check $x=8$
$\Rightarrow |20+2(8)|=|4(8)+4|$
$\Rightarrow |20+16|=|32+4|$
$\Rightarrow |36|=|36|$
$\Rightarrow 36=36$
True.
Check $x=-4$
$\Rightarrow |20+2(-4)|=|4(-4)+4|$
$\Rightarrow |20-8|=|-16+4|$
$\Rightarrow |12|=|-12|$
$\Rightarrow 12=12$
True.
Hence, the solutions are $x=8$ and $x=−4$.
