Question

solve for b and graph the solution. 15 ≥ |b - 90| + 5. click two endpoints to graph a line - segment, an endpoint and an arrow - head to graph a ray, or two arrow - heads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Isolate the absolute - value expression

Subtract 5 from both sides of the inequality $15\geq|b - 90|+5$.
$15−5\geq|b - 90|+5 - 5$, which simplifies to $10\geq|b - 90|$ or $|b - 90|\leq10$.

Step2: Solve the compound - inequality

The absolute - value inequality $|x|\leq a$ ($a\geq0$) is equivalent to $-a\leq x\leq a$. So, $|b - 90|\leq10$ is equivalent to $- 10\leq b - 90\leq10$.
Add 90 to all parts of the compound - inequality:
$-10+90\leq b-90 + 90\leq10 + 90$.
$80\leq b\leq100$.

Answer:

The solution of the inequality is $80\leq b\leq100$. On the number line, you would click on the points 80 and 100 and fill in the circle at both endpoints to represent the closed interval $[80,100]$.