Question

solve for b and graph the solution.
1 ≥ |b - 9|
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.
submit

Explanation:

Step1: Solve the absolute - value inequality

Given \(1\geq|b - 9|\). By the property of absolute - value \(|x|\leq a\) (\(a\geq0\)) is equivalent to \(-a\leq x\leq a\). Here \(x = b - 9\) and \(a = 1\), so \(-1\leq b-9\leq1\).
Add \(9\) to all parts of the compound inequality: \(-1 + 9\leq b-9 + 9\leq1 + 9\).

Step2: Simplify the inequality

\(8\leq b\leq10\)

Answer:

The solution of the inequality \(1\geq|b - 9|\) is \(8\leq b\leq10\). To graph it, place a filled - in circle at \(b = 8\) and \(b = 10\) and draw a line segment between them on the number line.