Answer
$w=3$ and $w=-\frac{1}{5}$
Work Step by Step
The given equation is
$\Rightarrow -2|5w−7|+9=-7$
Subtract $9$ from each side.
$\Rightarrow -2|5w−7|+9-9=-7-9$
Simplify.
$\Rightarrow -2|5w−7|=-16$
Divide each side by $-2$.
$\Rightarrow \frac{-2|5w−7|}{-2}=\frac{-16}{-2}$
Simplify.
$\Rightarrow |5w−7|=8$
Write related linear equations.
$\Rightarrow 5w−7=8$ or $5w−7=-8$
Add $7$ to each side.
$\Rightarrow 5w−7+7=8+7$ or $5w−7+7=-8+7$
Simplify.
$\Rightarrow 5w=15$ or $5w=-1$
Divide each side by $5$.
$\Rightarrow \frac{5w}{5}=\frac{15}{5}$ or $\frac{5w}{5}=-\frac{1}{5}$
Simplify.
$\Rightarrow w=3$ or $w=-\frac{1}{5}$
Check $w=3$
$\Rightarrow -2|5(3)−7|+9=-7$
$\Rightarrow -2|15−7|+9=-7$
$\Rightarrow -2|8|+9=-7$
$\Rightarrow -2(8)+9=-7$
$\Rightarrow -16+9=-7$
$\Rightarrow -7=-7$
True.
Check $x=-\frac{1}{5}$
$\Rightarrow -2|5(-\frac{1}{5})−7|+9=-7$
$\Rightarrow -2|-1−7|+9=-7$
$\Rightarrow -2|-8|+9=-7$
$\Rightarrow -2(8)+9=-7$
$\Rightarrow -16+9=-7$
$\Rightarrow -7=-7$
True.
Hence, the solutions are $w=3$ and $w=-\frac{1}{5}$.
