Question

solve for u and graph the solution.
1 ≥ |u + 7|
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 \(1\geq|u + 7|\) is equivalent to \(- 1\leq u+7\leq1\) because if \(|x|\leq a\) (\(a\geq0\)), then \(-a\leq x\leq a\).

Step2: Solve the compound inequality for \(u\)

Subtract 7 from all parts of the compound - inequality: \(-1-7\leq u + 7-7\leq1 - 7\).
\(-8\leq u\leq - 6\)

Answer:

The solution of the inequality is \(-8\leq u\leq - 6\). To graph it, click on the points at \(u=-8\) and \(u = - 6\) to create a line segment with filled - in endpoints (since the inequality includes the equal signs).