Question

Solve the inequality and graph the solution.
–
8≤4v
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 \(-8 \leq 4v\), we can start by isolating \(v\).

1. Divide both sides of the inequality by 4:

\[
\frac{-8}{4} \leq v
\]

This simplifies to:

\[
-2 \leq v
\]

or equivalently,

\[
v \geq -2
\]

The solution tells us that \(v\) can take any value greater than or equal to \(-2\).

### Graphing the Solution

1. **Endpoints**: The endpoint is \(v = -2\). Since \(v \geq -2\), we will represent this as a closed circle at \(-2\) because \(-2\) is included in the solution set.
2. **Ray**: After the endpoint \(-2\), we will draw a ray extending to the right (positive direction) to represent all values greater than \(-2\).

### Steps for Graphing:
- Draw the number line.
- Mark the point \(-2\) with a closed circle.
- Draw a solid arrow to the right from \(-2\).

### Change an Endpoint from Closed to Open:
In this case, there’s no need to change the closed endpoint at \(-2\) since it is included in the solution. However, if you were to change it for some reason (perhaps to explore what if), you would choose to delete the line extending to \(-2\) and change the closed circle at \(-2\) to an open circle (but note that this would not represent the original inequality correctly).

### Visual Representation:
- On the left side of the number line, you have the number line with the closed dot (•) at \(-2\).
- An arrow will extend indefinitely to the right, indicating that all values greater than \(-2\) are part of the solution.

This represents the solution to the inequality properly.