Question

Solve the inequality and graph the solution.
52(t+5)≤
–
52
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 \( 52(t + 5) \leq -52 \), follow these steps:

1. **Distribute**:
\[
52t + 260 \leq -52
\]

2. **Subtract 260 from both sides**:
\[
52t \leq -52 - 260
\]
\[
52t \leq -312
\]

3. **Divide by 52**:
\[
t \leq \frac{-312}{52}
\]
This simplifies to:
\[
t \leq -6
\]

So, the solution to the inequality is:
\[
t \leq -6
\]

### Graphing the solution:

- **Endpoint**: The endpoint of the interval is \( -6 \).
- **Closed circle**: Since the inequality is "less than or equal to," we will use a closed circle at \( -6 \).
- **Line/shade**: Shade to the left of \( -6 \) to indicate all values less than \( -6 \).

### Summary of the graph:

1. Plot a closed circle at \(-6\).
2. Shade the area to the left of \(-6\) to indicate all values less than or equal to \(-6\).

Here's a simple representation of how the graph would look:

```
<---●====================== (Graphical representation of the solution)
-8 -7 -6 -5 -4
```

In this graph, the closed circle at \(-6\) indicates that \(-6\) is included in the solution, and the shaded line to the left shows that all values less than \(-6\) are also included.