Answer
The solutions are $x=-6$ and $x=−2$.
Work Step by Step
The given equation is
$\Rightarrow |2x+6|=|x|$
Write related linear equations.
$\Rightarrow 2x+6=x$ or $2x+6=−x$
Solve the first equation.
$\Rightarrow 2x+6=x$
Add $-6-x$ to each side.
$\Rightarrow 2x+6-6-x=x-6-x$
Simplify.
$\Rightarrow x=-6$
Solve the second equation.
$\Rightarrow 2x+6=-x$
Add $-6+x$ to each side.
$\Rightarrow 2x+6-6+x=-x-6+x$
Simplify.
$\Rightarrow 3x=-6$
Divide each side by $3$.
$\Rightarrow \frac{3x}{3}=-\frac{6}{3}$
Simplify.
$\Rightarrow x=-2$
Check $x=-6$
$\Rightarrow |2x+6|=|x|$
$\Rightarrow |2(-6)+6|=|-6|$
$\Rightarrow |-12+6|=|-6|$
$\Rightarrow |-6|=|-6|$
$\Rightarrow 6=6$
True.
Check $x=-2$
$\Rightarrow |2x+6|=|x|$
$\Rightarrow |2(-2)+6|=|-2|$
$\Rightarrow |-4+6|=|-2|$
$\Rightarrow |2|=|-2|$
$\Rightarrow 2=2$
True.
Hence, the solutions are $x=-6$ and $x=−2$.
