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Let's solve the inequality:

\[
36 \leq 4x
\]

### Step 1: Solve for \( x \)
To isolate \( x \), divide both sides of the inequality by 4:

\[
\frac{36}{4} \leq \frac{4x}{4}
\]

\[
9 \leq x
\]

This simplifies to:

\[
x \geq 9
\]

### Step 2: Inequality Notation
The inequality notation is:

\[
x \geq 9
\]

### Step 3: Graph on the Number Line
On the number line, you will plot a closed dot at \( x = 9 \) (because the inequality includes \( x = 9 \), as indicated by the "greater than or equal to" symbol \( \geq \)). Then, shade the region to the right of 9, indicating all values greater than or equal to 9.

### Final Answer:
- **Inequality Notation**: \( x \geq 9 \)
- **Graph**: Closed dot at \( x = 9 \), with shading to the right of 9.

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

Here are 5 related questions to expand your understanding:
1. How do you graph inequalities with "<" or ">" on a number line?
2. What happens if you divide an inequality by a negative number?
3. How would the graph change if the inequality were \( 4x \leq 36 \)?
4. Can you explain how solving inequalities differs from solving equations?
5. How would you solve a compound inequality involving two inequality signs?

**Tip**: Always flip the inequality sign when multiplying or dividing both sides by a negative number!

Solve for x and graph the solution on the number line below: 36 ≤ 4x

Learn how to solve the linear inequality 36 ≤ 4x and graph the solution on a number line. This problem covers key algebraic concepts related to inequalities and is suitable for students in Grades 7-9. Detailed step-by-step solution provided.

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