Question

solve for q and graph the solution.
5 ≥ |q + 3|
click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Rewrite absolute - value inequality

The inequality \(5\geq|q + 3|\) is equivalent to \(-5\leq q+3\leq5\). This is because if \(|x|\leq a\) (\(a\geq0\)), then \(-a\leq x\leq a\).

Step2: Solve the compound - inequality for \(q\)

Subtract 3 from all parts of the compound - inequality \(-5\leq q + 3\leq5\). We get \(-5-3\leq q+3 - 3\leq5 - 3\), which simplifies to \(-8\leq q\leq2\).

Answer:

The solution set is \(-8\leq q\leq2\). To graph it, click on the points at \(q=-8\) and \(q = 2\) and make them filled - in circles (since the inequality includes the equal sign), and then click between them to create a line segment.