Answer
$d\leq -3$ or $d\geq 1$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 3|d+1|-7\geq -1$
Add $7$ to each side.
$\Rightarrow 3|d+1|-7+7\geq -1+7$
Simplify.
$\Rightarrow 3|d+1|\geq 6$
Divide each side by $3$.
$\Rightarrow \frac{3|d+1|}{3}\geq \frac{6}{3}$
Simplify.
$\Rightarrow |d+1|\geq 2$
Write a compound inequality.
$\Rightarrow d+1\leq -2$ or $d+1\geq 2$
Subtract $1$ from each side.
$\Rightarrow d+1-1\leq -2-1$ or $d+1-1\geq 2-1$
Simplify.
$\Rightarrow d\leq -3$ or $d\geq 1$
Hence, the solution is $d\leq -3$ or $d\geq 1$.
