Question

solve for b and graph the solution. |b - 7| ≥ 1 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: Recall absolute - value inequality rule

For \(|x|\geq a\) (\(a\geq0\)), the solution is \(x\geq a\) or \(x\leq - a\). Here \(x = b - 7\) and \(a = 1\), so \(b-7\geq1\) or \(b - 7\leq-1\).

Step2: Solve \(b - 7\geq1\)

Add 7 to both sides of the inequality: \(b-7 + 7\geq1 + 7\), which gives \(b\geq8\).

Step3: Solve \(b - 7\leq-1\)

Add 7 to both sides of the inequality: \(b-7 + 7\leq-1 + 7\), which gives \(b\leq6\).

Answer:

The solution is \(b\leq6\) or \(b\geq8\). On the number - line, we mark a closed circle at \(b = 6\) and draw an arrow to the left, and mark a closed circle at \(b = 8\) and draw an arrow to the right.