Question

Solve for xx and graph the solution on the number line below.
36, is greater than, minus, 9, x
36>
−9x
Answer
Attempt 1 out of 2


Inequality Notation:
Number Line:
Click and drag to plot line.
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12

Answer 1

To solve the inequality \( 36 > -9x \), you can first rewrite it in a more conventional form:

\[
-9x < 36
\]

Next, divide both sides by -9. Remember that when you divide an inequality by a negative number, you must reverse the inequality sign:

\[
x > \frac{36}{-9}
\]

Calculating the right-hand side gives:

\[
x > -4
\]

This means that the solution to the inequality is \( x > -4 \).

### Inequality Notation
The inequality notation is:
\[
x > -4
\]

### Number Line Graph
To graph this on the number line:
1. Draw an open circle at -4 (indicating that -4 is not included in the solution).
2. Shade the line to the right of -4 to indicate all numbers greater than -4.

Here’s an approximation of how it would look:

```
---|----|----|----|----|----|----|----|----|----|----|----|----|----
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
(------------------->
```
Here, the parenthesis at -4 indicates it is not included in the solution set, and the arrow indicates all numbers greater than -4.