Answer
$x=6$
Work Step by Step
The given equation is
$\Rightarrow |x+6|=2x$
Write related linear equations.
$\Rightarrow x+6=2x$ or $x+6=−2x$
Subtract $x$ from each side.
$\Rightarrow x+6-x=2x-x$ or $x+6-x=−2x-x$
Simplify.
$\Rightarrow 6=x$ or $6=−3x$
Solve for $x$.
$\Rightarrow 6=x$ or $-2=x$
Check $x=6$
$\Rightarrow |6+6|=2(6)$
$\Rightarrow |12|=12$
$\Rightarrow 12=12$
True.
Check $x=-2$
$\Rightarrow |-2+6|=2(-2)$
$\Rightarrow |4|=-4$
$\Rightarrow 4=-4$
false.
Hence, the solution is $x=6$.
