Question

solve for s and graph the solution. 13 ≥ |s + 65| + 8. 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: Isolate the absolute - value expression

Subtract 8 from both sides of the inequality $13\geq|s + 65|+8$.
$13-8\geq|s + 65|+8 - 8$, which simplifies to $5\geq|s + 65|$, or $|s + 65|\leq5$.

Step2: Rewrite the absolute - value inequality as a compound inequality

If $|x|\leq a$ ($a\geq0$), then $-a\leq x\leq a$. So, $|s + 65|\leq5$ becomes $-5\leq s+65\leq5$.

Step3: Solve the compound inequality for s

Subtract 65 from all parts of the compound inequality:
For the left - hand side: $-5-65\leq s+65 - 65$, which gives $-70\leq s$.
For the right - hand side: $s+65 - 65\leq5 - 65$, which gives $s\leq - 60$.

Answer:

The solution of the inequality is $-70\leq s\leq - 60$. To graph it, click on the points at $s=-70$ and $s = - 60$ to create a line segment with filled - in circles at both endpoints.