Question

Solve and graph the inequality.
-5x - 6 > 9

Answer 1

To solve the inequality \(-5x - 6 > 9\), follow these steps:

1. **Add 6 to both sides**:
\[
-5x - 6 + 6 > 9 + 6
\]
Simplifying gives:
\[
-5x > 15
\]

2. **Divide both sides by -5**. Remember that when you divide or multiply by a negative number, you must reverse the inequality sign:
\[
x < \frac{15}{-5}
\]
Simplifying gives:
\[
x < -3
\]

So the solution to the inequality is \(x < -3\).

### Graphing the Inequality:

1. Draw a number line.
2. Locate the point \(-3\) on the number line.
3. Since the inequality is \(x < -3\), draw an open circle at \(-3\) to indicate that \(-3\) is not included in the solution.
4. Shade the line to the left of \(-3\) to represent all numbers less than \(-3\).

Here is a representation of the graph:

```
<---(----|----|----|----|----|----|----|----->
-5 -4 -3 -2 -1 0 1 2
```
(The open circle at \(-3\) indicates that \(-3\) is not included in the solution, and the shading extends leftward.)