Question

Solve the inequality and graph the solution.
1≤
u+12
10
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 \( \frac{u + 12}{10} \geq 1 \), follow these steps:

1. Start by isolating \( u \):
\[
\frac{u + 12}{10} \geq 1
\]

2. Multiply both sides by 10 (since 10 is positive, the direction of the inequality does not change):
\[
u + 12 \geq 10
\]

3. Subtract 12 from both sides:
\[
u \geq 10 - 12
\]
\[
u \geq -2
\]

Thus, the solution to the inequality is:
\[
u \geq -2
\]

### Graphing the Solution

1. **Plot the endpoints**: The endpoint for this inequality is \( -2 \).
2. **Closed or open**: Since the inequality is \( \geq \), we will use a closed dot for \( -2 \).
3. **Graph the solution**: Shade the line to the right of \( -2 \) to indicate all values greater than or equal to \( -2 \).

The graph will look like this:

```
<---●====================>
-2
```

- The closed dot at \( -2 \) indicates that \( -2 \) is included in the solution.
- The shaded line to the right indicates all numbers greater than \( -2 \) are included in the solution.