Question

solve for u and graph the solution.
60 ≥ |3u - 30|
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: Solve the absolute - value inequality

Given \(60\geq|3u - 30|\). By the property of absolute - value inequalities \(|x|\leq a\) (where \(a\geq0\)) is equivalent to \(-a\leq x\leq a\). Here \(x = 3u-30\) and \(a = 60\), so \(-60\leq3u - 30\leq60\).

Step2: Solve the compound inequality

First, solve \(-60\leq3u - 30\):
Add \(30\) to all parts of the compound inequality. \(-60 + 30\leq3u-30 + 30\leq60 + 30\).
We get \(-30\leq3u\leq90\).
Then divide each part by \(3\): \(\frac{-30}{3}\leq\frac{3u}{3}\leq\frac{90}{3}\).
So \(- 10\leq u\leq30\).

Answer:

The solution of the inequality \(60\geq|3u - 30|\) is \(u\in[-10,30]\). On the number - line, we graph a line segment with endpoints at \(u=-10\) and \(u = 30\) (both endpoints are included, so we use filled - in circles).