https://file.aiquickdraw.com/mathbot/file/17260132192312501168p.jpg

The inequality in the image is \(6x > -18\). Let's solve it step by step:

### Step 1: Isolate \(x\)
To solve for \(x\), divide both sides of the inequality by 6:

\[
\frac{6x}{6} > \frac{-18}{6}
\]

\[
x > -3
\]

### Step 2: Graph the inequality
On a number line, you would place an open circle at \(x = -3\) because the inequality is strictly greater than (not "greater than or equal to"). Then, shade everything to the right of \(x = -3\), indicating all numbers greater than \(-3\).

### Graphing Details:
- The open circle at \(-3\) means that \(-3\) is not included in the solution.
- The shading to the right shows that any number larger than \(-3\) satisfies the inequality.

Would you like further details on how to graph this on a number line or any other clarification?

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Here are five related questions to help reinforce the concept:

1. How would the solution change if the inequality was \(6x \geq -18\)?
2. What happens to the inequality when you multiply or divide both sides by a negative number?
3. How do you graph an inequality with two sides, like \( -4 \leq x < 2 \)?
4. Can you solve and graph \( -5x < 15 \)?
5. What is the solution to \(7x + 2 \leq -12\)?

**Tip:** When solving inequalities, remember to reverse the inequality sign if you multiply or divide both sides by a negative number.

Solve and graph the inequality. Show your work and graph the inequality in the show your work part. Type the solution into the box. 6x > -18

Learn how to solve the inequality 6x > -18 by isolating x and graphing the solution on a number line. This problem covers key algebra concepts related to inequalities and is suitable for students in Grades 6-8.

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