Question

solve the compound inequality.
-5≤2x+1≤7
graph the solution on the number line.

Explanation:

Step1: Subtract 1 from all parts

$-5 - 1 \leq 2x + 1 - 1 \leq 7 - 1$
$-6 \leq 2x \leq 6$

Step2: Divide all parts by 2

$\frac{-6}{2} \leq \frac{2x}{2} \leq \frac{6}{2}$
$-3 \leq x \leq 3$

Step3: Graph setup explanation

On the number line, plot closed dots at $x=-3$ and $x=3$ (since the inequalities include equality), then shade the segment between these two points.

Answer:

The solution to the inequality is $\boldsymbol{-3 \leq x \leq 3}$.
For the graph: Mark closed (filled) dots at $-3$ and $3$ on the provided number line, and draw a solid line connecting these two points to represent all values between them.