Question

solve for v and graph the solution. |v + 5| < 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: Recall absolute value inequality rule

For $|x| < a$ (where $a > 0$), the solution is $-a < x < a$. So for $|v + 5| < 4$, we apply this rule: $-4 < v + 5 < 4$.

Step2: Solve the left inequality

Subtract 5 from all parts: $-4 - 5 < v + 5 - 5 < 4 - 5$.
Simplify: $-9 < v < -1$.
To graph, we use open circles at $v = -9$ and $v = -1$ (since the inequality is strict, $<$ not $\leq$) and draw a line segment between them on the number line.

Answer:

$-9 < v < -1$