Answer
$x=9$ and $x=−3$
Work Step by Step
The given equation is
$\Rightarrow 2|x−3|-5=7$
Add $5$ to each side.
$\Rightarrow 2|x−3|-5+5=7+5$
Simplify.
$\Rightarrow 2|x−3|=12$
Divide each side by $2$.
$\Rightarrow \frac{2|x−3|}{2}=\frac{12}{2}$
Simplify.
$\Rightarrow |x−3|=6$
Write related linear equations.
$\Rightarrow x−3=6$ or $x−3=−6$
Add $3$ to each side.
$\Rightarrow x−3+3=6+3$ or $x−3+3=−6+3$
Simplify.
$\Rightarrow x=9$ or $x=−3$
Check $x=9$
$\Rightarrow 2|9−3|-5=7$
$\Rightarrow 2|6|-5=7$
$\Rightarrow 2(6)-5=7$
$\Rightarrow 12-5=7$
$\Rightarrow 7=7$
True.
Check $x=-3$
$\Rightarrow 2|-3−3|-5=7$
$\Rightarrow 2|-6|-5=7$
$\Rightarrow 2(6)-5=7$
$\Rightarrow 12-5=7$
$\Rightarrow 7=7$
True.
Hence, the solutions are $x=9$ and $x=−3$.
