Answer
The solution set is $\{-\frac{11}{2},\frac{23}{2}\}$.
Work Step by Step
The given equation is
$2\left | x-3 \right |-7=10$
Add $7$ to both sides.
$2\left | x-3 \right |-7+7=10+7$
Simplify.
$2\left | x-3 \right |=17$
Divide both sides by $2$.
$\frac{2\left | x-3 \right |}{2}=\frac{17}{2}$
Simplify.
$\left | x-3 \right |=\frac{17}{2}$
Remove the absolute value bars.
$ x-3 =-\frac{17}{2}$ or $ x-3 =\frac{17}{2}$
Add $3$ to both sides.
$ x-3+3 =-\frac{17}{2}+3$ or $ x-3+3 =\frac{17}{2}+3$
Simplify.
$ x=\frac{-17+6}{2}$ or $ x =\frac{17+6}{2}$
$ x=\frac{-11}{2}$ or $ x =\frac{23}{2}$.
