Question

Use the number line to represent the solution to 2.4x - 6 > - 13.2

Answer 1

To solve the inequality \( 2.4x - 6 > -13.2 \), follow these steps:

1. **Add 6 to both sides:**
\[
2.4x - 6 + 6 > -13.2 + 6
\]
This simplifies to:
\[
2.4x > -7.2
\]

2. **Divide both sides by 2.4:**
\[
x > \frac{-7.2}{2.4}
\]
Calculating the division:
\[
x > -3
\]

Now, the solution to the inequality is \( x > -3 \).

### Number Line Representation
To represent this solution on a number line:

1. Draw a horizontal line (this will be your number line).
2. Mark and label the point \(-3\) on the number line.
3. Since the inequality is \(x > -3\) (not including -3), use an open circle at \(-3\) to indicate that -3 is not part of the solution.
4. Shade the line to the right of \(-3\) to show that all values greater than -3 are included in the solution set.

Here's a simple representation:

```
<-∞----(-3)----|----|----|----|----|----|----|----|----|----|---->∞
O
```

The open circle at \(-3\) indicates the value is not included in the solution, and the arrow indicates that the values extending to the right (greater than \(-3\)) are part of the solution.