Question

solve for b and graph the solution. |b - 88| ≤ 5. 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. solve absolute value inequalities (90) not feeling ready yet? these can help: work it out graph inequalities

Explanation:

Step1: Recall absolute - value inequality rule

If \(|x|\leq a\) (\(a\geq0\)), then \(-a\leq x\leq a\). For \(|b - 88|\leq5\), we have \(- 5\leq b - 88\leq5\).

Step2: Add 88 to all parts of the compound - inequality

Adding 88 to \(-5\leq b - 88\leq5\), we get \(-5+88\leq b-88 + 88\leq5 + 88\).
So, \(83\leq b\leq93\).

Step3: Graph the solution on the number - line

On the number - line, we mark the points 83 and 93. Since the inequality is \(\leq\), we use filled - in circles at 83 and 93 and draw a line segment between them.

Answer:

The solution of the inequality is \(83\leq b\leq93\). On the number - line, mark filled - in circles at 83 and 93 and draw a line segment connecting them.