Question

solve for w and graph the solution.
20 ≥ |w + 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: Rewrite absolute - value inequality

The inequality \(20\geq|w + 30|\) is equivalent to \(-20\leq w+30\leq20\) because if \(|a|\leq b\) (\(b\geq0\)), then \(-b\leq a\leq b\).

Step2: Solve the left - hand side of the compound inequality

Subtract 30 from all parts of \(-20\leq w + 30\leq20\). For the left - hand side, \(-20-30\leq w+30 - 30\), which simplifies to \(-50\leq w\).

Step3: Solve the right - hand side of the compound inequality

For the right - hand side, \(w+30-30\leq20 - 30\), which simplifies to \(w\leq - 10\).

Answer:

The solution of the inequality is \(-50\leq w\leq - 10\). On the number line, you would click on the points at \(w=-50\) and \(w = - 10\) and make them filled - in circles (since the inequality includes the equal sign), and then click between them to graph the line segment.