Solve for xx and graph the solution on the number line below.

Question

−72>
−9x

Answer 1

To solve for \( x \), you need to isolate \( x \) on one side of the inequality.

The inequality is \( -72 > -9x \).

First, we divide both sides by \( -9 \) to solve for \( x \). However, when dividing by a negative number in an inequality, the inequality sign flips.

\[
\frac{-72}{-9} < \frac{-9x}{-9}
\]

This simplifies to:

\[
8 < x
\]

This means that \( x \) is any number greater than 8.

To graph the solution on the number line, you will draw an open circle at 8 to indicate that 8 is not included in the solution and draw an arrow to the right of 8 to indicate that the solution includes all numbers greater than 8:

```
|------|------|------|------|------|------|--->
... 6 7 8 9 10 11 ...
o
```

The open circle at 8 shows that 8 is not part of the solution, and the line with the arrow indicates all numbers greater than 8.