Answer
$-\frac{7}{3}\lt g \lt 1$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow |-3g-2|+1\lt 6$
Subtract $1$ from each side.
$\Rightarrow |-3g-2|+1-1\lt 6-1$
Simplify.
$\Rightarrow |-3g-2|\lt 5$
Write a compound inequality.
$\Rightarrow -3g-2\lt 5$ and $-3g-2\gt -5$
Add $2$ to each side.
$\Rightarrow -3g-2+2\lt 5+2$ and $-3g-2+2\gt -5+2$
Simplify.
$\Rightarrow -3g\lt 7$ and $-3g\gt -3$
Divide each side by $-3$. Reverse the inequality symbol.
$\Rightarrow \frac{-3g}{-3}\gt \frac{7}{-3}$ and $\frac{-3g}{-3}\lt \frac{-3}{-3}$
Simplify.
$\Rightarrow g\gt -\frac{7}{3}$ and $g\lt 1$
Hence, the solution is $-\frac{7}{3}\lt g \lt 1$.