Question

Solve for xx and graph the solution on the number line below.
minus, 72, is greater than, minus, 9, x
−72>
−9x

Answer 1

To solve the inequality -72 > -9x, you want to isolate x. To do this, divide both sides by -9. When dividing or multiplying both sides of an inequality by a negative number, the inequality sign flips.

-72 / -9 > -9x / -9

8 < x

This is read as "x is greater than 8."

Now, let's graph this on a number line:

```
----|----|----|----|----|----|----|----|----|----|---->
... 6 7 8 9 10 11 12 13 14 15 ...
```

To graph x > 8 on the number line:

1. Draw a circle around 8 to indicate that 8 is not included in the solution (because the inequality is strictly "greater than").
2. Draw a line or arrow to the right of 8 to indicate that the solution includes all numbers greater than 8.

Here's a visual representation with an open circle at 8 and the line extending to the right:

```
( )
----|----|----|----|----|----|----|----|----|----|---->
... 6 7 8 9 10 11 12 13 14 15 ...
```

The above "number line" is a textual representation. The actual number line would have a continuous line, with an open circle at 8, and the line heading to the right, towards higher numbers, to indicate that the solution includes all numbers greater than 8.