Question

solve for v and graph the solution.
4 ≥ |v + 5|
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: Solve the absolute - value inequality

Given \(4\geq|v + 5|\). Since \(|a|\leq b\) (where \(b\geq0\)) is equivalent to \(-b\leq a\leq b\), we have \(-4\leq v + 5\leq4\).

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

Subtract 5 from both sides of \(-4\leq v + 5\): \(-4-5\leq v+5 - 5\), which simplifies to \(-9\leq v\).

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

Subtract 5 from both sides of \(v + 5\leq4\): \(v+5 - 5\leq4 - 5\), which simplifies to \(v\leq - 1\).

Answer:

The solution is \(-9\leq v\leq - 1\). On the number line, the graph has a filled - in circle at \(v=-9\), a filled - in circle at \(v = - 1\), and a line segment connecting them.