https://file.aiquickdraw.com/mathbot/file/17266642850665171nxut.jpg

Let's solve the inequality shown in the image:

\[
-72 > -9x
\]

### Step 1: Isolate the variable
To solve for \( x \), we first divide both sides of the inequality by \(-9\). **Important**: When dividing an inequality by a negative number, the inequality sign flips.

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

Simplifying:

\[
8 < x
\]

This can also be written as:

\[
x > 8
\]

### Step 2: Write the inequality notation
The solution to this inequality is:

\[
x > 8
\]

### Step 3: Graphing on a number line
On the number line, the value of \( x \) is all the numbers greater than 8. This means:

- You will have an open circle at \( x = 8 \) (because \( x \) is not equal to 8, just greater than).
- Shade everything to the right of 8 to indicate that \( x \) can be any number greater than 8.

Would you like further clarification on this, or do you have any questions? 

Here are 5 related questions to deepen your understanding:

1. What happens to the inequality symbol when you multiply or divide by a negative number?
2. How would the solution change if the inequality was \( -72 \geq -9x \)?
3. Can you think of a real-life situation where solving inequalities might be necessary?
4. How can you verify the solution of this inequality using a specific value of \( x \)?
5. What is the difference between a strict inequality (like \( x > 8 \)) and a non-strict inequality (like \( x \geq 8 \))?

**Tip**: Always remember to flip the inequality sign when dividing or multiplying by a negative number.

Solve for x and graph the solution on the number line: -72 > -9x

Learn how to solve the inequality -72 > -9x by dividing both sides by -9, remembering to flip the inequality sign. The solution, x > 8, is then graphed on a number line with an open circle at 8, shading everything to the right. Ideal for Grades 7-9 students.

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