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Let's solve the compound inequality step by step and then graph the solution on the number line.

### Given inequalities:
1. \( 3x + 6 \geq 18 \)
2. \( 4x - 4 \leq 0 \)

#### 1. Solving \( 3x + 6 \geq 18 \):
- Subtract 6 from both sides:
  \[
  3x \geq 12
  \]
- Divide both sides by 3:
  \[
  x \geq 4
  \]

#### 2. Solving \( 4x - 4 \leq 0 \):
- Add 4 to both sides:
  \[
  4x \leq 4
  \]
- Divide both sides by 4:
  \[
  x \leq 1
  \]

### Compound Inequality Solution:
The solution is \( x \geq 4 \) **or** \( x \leq 1 \). 

This represents two separate regions:
- \( x \geq 4 \): The values of \( x \) are 4 and greater.
- \( x \leq 1 \): The values of \( x \) are 1 and smaller.

### Graphing on the number line:
- For \( x \geq 4 \), you will use a filled circle at 4 and shade the number line to the right (towards positive infinity).
- For \( x \leq 1 \), you will use a filled circle at 1 and shade the number line to the left (towards negative infinity).

Would you like more details on any part of this, or would you like me to proceed with additional questions?

Here are five related questions:
1. How do you solve compound inequalities involving "and" versus "or"?
2. What is the difference between strict inequalities and non-strict inequalities?
3. How would you graph \( x \geq 4 \) or \( x < 0 \) on a number line?
4. Can a solution to a compound inequality be a single value?
5. What are some common mistakes to avoid when solving compound inequalities?

**Tip:** Always check the boundary points of inequalities when graphing to ensure whether to use an open or closed circle.

Solve the compound inequality: 3x + 6 ≥ 18 or 4x - 4 ≤ 0. Graph the solution on the number line.

Learn how to solve the compound inequality 3x + 6 ≥ 18 or 4x - 4 ≤ 0 with a step-by-step solution. This guide covers key algebra concepts including solving inequalities, applying basic operations, and graphing the solution on a number line. Suitable for students in Grades 8-10.

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