Question

Solve the inequality and graph the solution on the line provided.
minus, 7, plus, 7, x, is less than or equal to, minus, 14
−7+7x≤
−14

Answer 1

To solve the inequality \( -7 + 7x \leq -14 \), follow these steps:

1. **Add 7 to both sides of the inequality**:
\[
-7 + 7x + 7 \leq -14 + 7
\]
This simplifies to:
\[
7x \leq -7
\]

2. **Divide both sides by 7**:
\[
x \leq -1
\]

The solution to the inequality is \( x \leq -1 \).

### Graphing the Solution

To graph this solution on a number line:

- Draw a number line and include the point -1.
- Since the inequality is \( \leq \), you will place a solid dot on -1 to indicate that -1 is included in the solution set.
- Shade the line to the left of -1 to indicate all numbers less than -1 are included in the solution.

Here's how you would represent it visually:

```
<---●-------|-------|-------|-------|-------|-------|------->
-3 -2 -1 0 1 2 3
```

The dot on -1 is solid, indicating that -1 is included in the solution. The shading extends to the left, covering all values less than -1.