Question

solve for b and graph the solution. |b - 74| ≥ 2 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 absolute - value inequality \(|b - 74|\geq2\) can be rewritten as two separate inequalities: \(b−74\geq2\) or \(b - 74\leq - 2\).

Step2: Solve \(b−74\geq2\)

Add 74 to both sides of the inequality: \(b-74 + 74\geq2 + 74\), so \(b\geq76\).

Step3: Solve \(b - 74\leq - 2\)

Add 74 to both sides of the inequality: \(b-74 + 74\leq - 2+74\), so \(b\leq72\).

Answer:

The solution is \(b\leq72\) or \(b\geq76\). On the number - line, there will be a ray starting from 72 (filled circle) going to the left and a ray starting from 76 (filled circle) going to the right.