Question

Solve the inequality and graph the solution.
2(v+14)–17>3
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 \( 2(v+14) - 17 > 3 \), we can follow these steps:

1. **Distribute and simplify**:
\[
2(v + 14) - 17 > 3
\]
Distributing \( 2 \):
\[
2v + 28 - 17 > 3
\]
Simplifying:
\[
2v + 11 > 3
\]

2. **Subtract 11 from both sides**:
\[
2v > 3 - 11
\]
\[
2v > -8
\]

3. **Divide by 2**:
\[
v > -4
\]

Thus, the solution to the inequality is \( v > -4 \).

### Graphing the solution:
- The solution includes all numbers greater than \(-4\).
- Since \(-4\) is not included in the solution, we will represent it with an open circle at \(-4\).
- The ray will extend to the right from \(-4\).

Here is a simple representation of the graph:

```
----|---------|---------|---------|---------
-5 -4 -3 -2
```
- Place an open circle at \(-4\):
```
----|---------o---------|---------|---------
-5 -4 -3 -2
```
- Shade to the right of \(-4\) to indicate all values greater than \(-4\):
```
----|---------o=========|---------|---------
-5 -4 -3 -2
```

This illustrates the range of values that satisfy the inequality \( v > -4 \).