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

Question

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.