Answer
$-10\lt x\lt 5$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow -12\lt \frac{1}{2}(4x+16) \lt 18$
Multiply each side by $2$.
$\Rightarrow 2(-12)\lt 2( \frac{1}{2})(4x+16) \lt 2(18)$
Simplify.
$\Rightarrow -24\lt 4x+16 \lt 36$
Subtract $16$ from each expression.
$\Rightarrow -24-16\lt 4x+16-16 \lt 36-16$
Simplify.
$\Rightarrow -40\lt 4x\lt 20$
Divide each side by $4$.
$\Rightarrow \frac{-40}{4}\lt \frac{4x}{4}\lt \frac{20}{4}$
Simplify.
$\Rightarrow -10\lt x\lt 5$
Hence, the solution is $-10\lt x\lt 5$.
