Question

Solve the inequality and graph the solution.
v+1
3
≥
–
1
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality

\[
\frac{v + 1}{3} \geq -1,
\]

we start by isolating \( v \).

1. Multiply both sides of the inequality by 3 to eliminate the fraction (note that since 3 is positive, the direction of the inequality does not change):

\[
v + 1 \geq -3.
\]

2. Next, subtract 1 from both sides:

\[
v \geq -4.
\]

Now, we have the solution to the inequality, which is

\[
v \geq -4.
\]

### Graphing the Solution:

1. Plot the endpoint at \( v = -4 \). Since the inequality includes \( \geq \), we will use a closed dot on -4 to indicate that -4 is included in the solution set.

2. Draw a ray extending to the right from -4 to indicate that all values greater than -4 are included in the solution.

### Final Graph Summary:
- Closed dot at \( -4 \)
- Shade the line to the right of -4.

This represents all values \( v \) such that \( v \) is greater than or equal to -4.