Question

Solve for x and graph the solution on the number line below. -64›8x. Make sure to include how to shade the number line and include the inequality notion

Answer 1

To solve the inequality \(-64 > 8x\), we can follow these steps:

1. **Isolate the variable \(x\)**: We want to solve for \(x\) by dividing both sides of the inequality by 8.

\[
\frac{-64}{8} > x
\]
\[
-8 > x
\]

This can also be rewritten as:
\[
x < -8
\]

2. **Graph the solution on a number line**: To represent the solution \(x < -8\) on a number line:
- Draw a number line with a range that clearly includes the number -8.
- Use an open circle at -8 to indicate that -8 is not included in the solution (because the inequality is strictly less than).
- Shade the line to the left of -8 to indicate all numbers less than -8 are included in the solution.

Here’s an example of how the number line would look:

```
<---|----|----|----|----|----|----|----|----|----|--->
-10 -9 -8 -7 -6 -5 -4 -3 -2
O
<----------------
```

- In the graph:
- **O** at -8 is an open circle, indicating that -8 is not part of the solution.
- The shading to the left indicates that all values less than -8 satisfy the inequality.

Thus, the solution to the inequality \(-64 > 8x\) is \(x < -8\).