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.