Question

Solve the inequality and graph the solution.
5(y–2)<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 \(5(y - 2) < 10\), we will follow these steps:

1. **Distribute and simplify**:
\[
5y - 10 < 10
\]

2. **Add 10 to both sides**:
\[
5y < 20
\]

3. **Divide by 5**:
\[
y < 4
\]

The solution to the inequality is \(y < 4\).

### Graphing the solution:

- **Endpoints**: The endpoint here is \(y = 4\). We will plot the point \(4\) on the number line.
- **Open vs. closed endpoint**: Since \(y\) is less than \(4\) (not including \(4\)), we will use an open circle at \(4\).
- **Direction**: The inequality \(y < 4\) indicates all values less than \(4\), so we shade to the left of \(4\).

### Graph representation:
On a number line:

1. Draw an empty circle at \(4\) (open endpoint).
2. Shade the line to the left of \(4\).

Here’s a simple representation:

```
-----o========================>
4
```

The open circle at \(4\) indicates that \(4\) is not included in the solution set, and the shaded part indicates all values less than \(4\) are included.