Question

solve for b and graph the solution. |b - 830| ≤ 40 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: Apply absolute - value inequality rule

For \(|x|\leq a\), the solution is \(-a\leq x\leq a\). Here \(x = b - 830\) and \(a = 40\), so \(-40\leq b-830\leq40\).

Step2: Solve the compound inequality

Add \(830\) to all parts: \(-40 + 830\leq b-830 + 830\leq40+830\).
\(790\leq b\leq870\).

Answer:

The solution for \(b\) is \(790\leq b\leq870\). On the number - line, click on the point \(790\) (filled - in circle) and the point \(870\) (filled - in circle) to graph the line segment.