Answer
$x=-\frac{3}{2}$ and $x=-\frac{11}{2}$
Work Step by Step
The given equation is
$\Rightarrow 4|2x+7|=16$
Divide each side by $4$.
$\Rightarrow \frac{4|2x+7|}{4}=\frac{16}{4}$
Simplify.
$\Rightarrow |2x+7|=4$
Write related linear equations.
$\Rightarrow 2x+7=4$ or $2x+7=−4$
Subtract $7$ from each side.
$\Rightarrow 2x+7-7=4-7$ or $2x+7-7=−4-7$
Simplify.
$\Rightarrow 2x=-3$ or $2x=−11$
Divide each side by $2$.
$\Rightarrow \frac{2x}{2}=-\frac{3}{2}$ or $\frac{2x}{2}=−\frac{11}{2}$
Simplify.
$\Rightarrow x=-\frac{3}{2}$ or $x=−\frac{11}{2}$
Check $x=-\frac{3}{2}$
$\Rightarrow 4|2(-\frac{3}{2})+7|=16$
$\Rightarrow 4|-3+7|=16$
$\Rightarrow 4|4|=16$
$\Rightarrow 4(4)=16$
$\Rightarrow 16=16$
True.
Check $x=-\frac{11}{2}$
$\Rightarrow 4|2(-\frac{11}{2})+7|=16$
$\Rightarrow 4|-11+7|=16$
$\Rightarrow 4|-4|=16$
$\Rightarrow 4(4)=16$
$\Rightarrow 16=16$
True.
Hence, the solutions are $x=-\frac{3}{2}$ and $x=-\frac{11}{2}$.
