Question

graph the solution to the inequality on the number line.
|u + 3| ≤ 5

Explanation:

Step1: Rewrite absolute - value inequality

If \(|a|\leq b\) (\(b\geq0\)), then \(-b\leq a\leq b\). So for \(|u + 3|\leq5\), we have \(-5\leq u+3\leq5\).

Step2: Solve the compound inequality

Subtract 3 from all parts of the compound - inequality: \(-5-3\leq u+3 - 3\leq5 - 3\).
\(-8\leq u\leq2\).

Step3: Graph on number line

On the number line, we mark a closed circle at \(-8\) (because \(u\) can equal \(-8\)) and a closed circle at 2 (because \(u\) can equal 2), and then shade the region between them.

Answer:

Graph a closed - circle at \(-8\), a closed - circle at 2, and shade the region between \(-8\) and 2 on the number line.