https://file.aiquickdraw.com/mathbot/file/1726625444038lz0l80z5.jpg

The inequality in the image is:

\[
n - 2(n - 12) \leq 5n
\]

Let's solve this step by step.

### Step 1: Expand the terms on the left side
Distribute the \(-2\) across \((n - 12)\):

\[
n - 2(n - 12) = n - 2n + 24
\]

So the inequality becomes:

\[
n - 2n + 24 \leq 5n
\]

### Step 2: Simplify the left side
\[
-n + 24 \leq 5n
\]

### Step 3: Move all terms involving \(n\) to one side
Add \(n\) to both sides to isolate the terms involving \(n\):

\[
24 \leq 6n
\]

### Step 4: Solve for \(n\)
Divide both sides by 6:

\[
n \geq 4
\]

### Final Inequality:
\[
n \geq 4
\]

### Solution in Interval Form:
\[
[4, \infty)
\]

### Solution on the Number Line:
- The solution includes 4 (closed circle at 4) and all numbers greater than 4. The graph would show a line extending to the right from 4, indicating all numbers larger than or equal to 4.

Would you like a graphical representation, further details, or have any questions?

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Here are some related questions:
1. How do we handle inequalities involving absolute values?
2. What is the difference between a strict inequality and a non-strict inequality?
3. How can you verify solutions of an inequality?
4. How would the solution change if the inequality was \(n - 2(n - 12) > 5n\)?
5. What happens if you divide by a negative number in an inequality?

**Tip**: Always remember, when you multiply or divide both sides of an inequality by a negative number, the inequality sign flips!

Solve the inequality: n - 2(n - 12) ≤ 5n, and provide the solution set in both interval and graph form.

Learn how to solve the inequality n - 2(n - 12) ≤ 5n, and find the solution set in interval form. Explore step-by-step algebraic methods, including the distributive property and solving inequalities. Suitable for Grades 7-9.

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