Answer
$c\lt -3$ or $c\gt \frac{1}{2}$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow |4c+5|\gt7$
Write a compound inequality.
$\Rightarrow 4c+5\lt -7$ or $4c+5\gt 7$
Subtract $5$ from each side.
$\Rightarrow 4c+5-5\lt -7-5$ or $4c+5-5\gt 7-5$
Simplify.
$\Rightarrow 4c\lt -12$ or $4c\gt 2$
Divide each side by $4$.
$\Rightarrow \frac{4c}{4}\lt \frac{-12}{4}$ or $\frac{4c}{4}\gt \frac{2}{4}$
Simplify.
$\Rightarrow c\lt -3$ or $c\gt \frac{1}{2}$
Hence, the solution is $c\lt -3$ or $c\gt \frac{1}{2}$.
