Question

solve for v and graph the solution.
7> |v + 7| + 4
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: Simplify the inequality

Subtract 4 from both sides of \(7 > |v + 7|+4\).
\(7-4>|v + 7|+4 - 4\), so \(3>|v + 7|\), which can be written as \(|v + 7|<3\).

Step2: Solve the absolute - value inequality

Recall that if \(|x|0\)), then \(-aFor \(|v + 7|<3\), we have \(-3Subtract 7 from all parts of the compound inequality:
\(-3-7\(-10

Answer:

The solution of the inequality is \(v\in(-10,-4)\). On the number - line, we click on \(-10\) (make it an empty circle) and \(-4\) (make it an empty circle) and then click between them to graph the line segment.