Answer
$\left\{ -2,7\right \}$.
Work Step by Step
The given equation is
$\Rightarrow 3- \left | 2x-5\right |=-6$
Subtract $3$ from both sides.
$\Rightarrow 3- \left | 2x-5\right |-3=-6-3$
Simplify.
$\Rightarrow - \left | 2x-5\right |=-9$
Multiply by $-1$ on both sides.
$\Rightarrow -1(- \left | 2x-5\right |)=-1(-9)$
Simplify.
$\Rightarrow \left | 2x-5\right |=9$
Rewrite the equation without absolute value bars.
$\Rightarrow 2x-5=9$ or $2x-5=-9$
Solve both equations separately.
First equation.
$\Rightarrow 2x-5=9$
Add $5$ to both sides.
$\Rightarrow 2x-5+5=9+5$
Add like terms.
$\Rightarrow 2x=14$
Divide both sides by $2$.
$\Rightarrow \frac{2x}{2}=\frac{14}{2}$
Simplify.
$\Rightarrow x=7$
Second equation.
$\Rightarrow 2x-5=-9$
Add $5$ to both sides.
$\Rightarrow 2x-5+5=-9+5$
Add like terms.
$\Rightarrow 2x=-4$
Divide both sides by $2$.
$\Rightarrow \frac{2x}{2}=\frac{-4}{2}$
Simplify.
$\Rightarrow x=-2$
Hence, the solution set is $\left\{ -2,7\right \}$.
