Question

Solve the inequality and graph the solution.
8y–2≤
–
10
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

Answer 1

To solve the inequality \( 8y - 2 \leq -10 \), follow these steps:

1. **Isolate the variable \( y \)**:

Add 2 to both sides:
\[
8y - 2 + 2 \leq -10 + 2
\]
Simplifying gives:
\[
8y \leq -8
\]

2. **Divide by 8**:

Divide both sides by 8 (note that since 8 is positive, the inequality direction will not change):
\[
y \leq -1
\]

So, the solution to the inequality is:
\[
y \leq -1
\]

### Graphing the Solution

1. **Plot the point** \( -1 \) on a number line.
2. **Since the inequality is \( \leq \)**, use a **closed circle** on \( -1 \) to indicate that this value is included in the solution.
3. **Draw a ray** to the left of \( -1 \) to indicate that all values less than \(-1\) are also included in the solution.

This graphic representation shows that all numbers less than or equal to \(-1\) satisfy the inequality.

If you were creating the graph visually, it would look like this:

```
<---•=========================
-2 -1 0 1
```

Here, the dot at \(-1\) is filled in, indicating that \(-1\) is included in the solution. The line continues to the left, showing all values less than \(-1\).