Question

solve for v and graph the solution.
|v - 70| ≤ 25
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: Apply absolute - value inequality rule

If \(|x|\leq a\) (\(a\geq0\)), then \(-a\leq x\leq a\). For \(|v - 70|\leq25\), we have \(- 25\leq v-70\leq25\).

Step2: Solve the compound inequality

Add \(70\) to all parts of the compound inequality.
For the left - hand side: \(-25 + 70\leq v-70 + 70\), which simplifies to \(45\leq v\).
For the right - hand side: \(v-70 + 70\leq25 + 70\), which simplifies to \(v\leq95\).

Answer:

The solution of the inequality \(|v - 70|\leq25\) is \(45\leq v\leq95\). On the number line, we click on the point \(45\) (filled - in circle) and the point \(95\) (filled - in circle) to graph the line segment representing the solution set.