Answer
$h\lt7 $ or $h\gt 11$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow -5\lt 2-h$ or $6h+5 \gt 71$
Solve the first inequality.
$\Rightarrow -5\lt 2-h$
Add $h$ to each side.
$\Rightarrow -5+h\lt 2-h+h$
Simplify.
$\Rightarrow -5+h\lt 2$
Add $5$ to each side.
$\Rightarrow -5+h+5\lt 2+5$
Simplify.
$\Rightarrow h\lt 7$
Solve the second inequality.
$\Rightarrow 6h+5 \gt 71$
Subtract $5$ from each side.
$\Rightarrow 6h+5 -5\gt 71-5$
Simplify.
$\Rightarrow 6h\gt 66$
Divide each side by $6$.
$\Rightarrow \frac{6h}{6}\gt \frac{66}{6}$
Simplify.
$\Rightarrow h\gt 11$
Hence, the solution is $h\lt7 $ or $h\gt 11$.
