Question

solve for s and graph the solution. -45 ≤ -3|s + 35| 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: Divide both sides by -3

When dividing an inequality by a negative number, the inequality sign flips. So, \(\frac{-45}{-3}\geq\frac{-3|s + 35|}{-3}\), which simplifies to \(15\geq|s+35|\).

Step2: Rewrite the absolute - value inequality

The inequality \(|s + 35|\leq15\) can be rewritten as \(-15\leq s+35\leq15\).

Step3: Subtract 35 from all parts of the compound inequality

For the left - hand side: \(-15-35\leq s+35 - 35\), which gives \(-50\leq s\). For the right - hand side: \(s+35-35\leq15 - 35\), which gives \(s\leq - 20\).

Answer:

The solution is \(-50\leq s\leq - 20\). On the number line, we click on the points \(-50\) (filled - in circle) and \(-20\) (filled - in circle) and draw a line segment between them.