Question

solve for b and graph the solution. 16 ≥ |-4b + 64| 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 inequality $16\geq|-4b + 64|$ is equivalent to $-16\leq-4b + 64\leq16$.

Step2: Solve the left - hand side of the compound inequality

Solve $-16\leq-4b + 64$.
Subtract 64 from both sides: $-16-64\leq-4b$, so $-80\leq-4b$.
Divide both sides by - 4 and reverse the inequality sign: $20\geq b$.

Step3: Solve the right - hand side of the compound inequality

Solve $-4b + 64\leq16$.
Subtract 64 from both sides: $-4b\leq16 - 64$, so $-4b\leq-48$.
Divide both sides by - 4 and reverse the inequality sign: $b\geq12$.

Answer:

The solution is $12\leq b\leq20$. To graph, click on 12 and 20 and make them filled - in circles, then click between them to create a line segment.