https://file.aiquickdraw.com/mathbot/file/1725542137956y4rntzrm.jpg

The image shows a compound inequality problem. Here's how we can solve it:

### Problem:
Solve the compound inequality:

\[
3x + 1 \geq 13 \quad \text{or} \quad 4x + 4 \leq -8
\]

And graph the solution on the number line.

---

### Step 1: Solve each inequality separately.

#### For the first inequality: \( 3x + 1 \geq 13 \)
1. Subtract 1 from both sides:
   \[
   3x \geq 12
   \]
2. Divide by 3:
   \[
   x \geq 4
   \]

#### For the second inequality: \( 4x + 4 \leq -8 \)
1. Subtract 4 from both sides:
   \[
   4x \leq -12
   \]
2. Divide by 4:
   \[
   x \leq -3
   \]

---

### Step 2: Combine the results.

This is an "or" compound inequality, so the solution is any \(x\) that satisfies either inequality.

- \( x \geq 4 \) (all values greater than or equal to 4)
- \( x \leq -3 \) (all values less than or equal to -3)

### Step 3: Graph the solution.

On the number line, we will mark:
- A closed circle at \( x = 4 \) with an arrow pointing to the right (indicating values greater than or equal to 4).
- A closed circle at \( x = -3 \) with an arrow pointing to the left (indicating values less than or equal to -3).

This represents two separate regions on the number line.

Would you like me to clarify any part of the process? Here are some related questions to expand your understanding:

1. How do you solve inequalities that involve fractions?
2. What happens when inequalities are combined with "and" instead of "or"?
3. How do you graph inequalities on a number line?
4. How does multiplying or dividing by a negative number affect inequality signs?
5. Can inequalities have more than one solution?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing by a negative number.

Solve the compound inequality: 3x + 1 ≥ 13 or 4x + 4 ≤ -8. Graph the solution on the number line.

Learn how to solve and graph the compound inequality 3x + 1 ≥ 13 or 4x + 4 ≤ -8 with detailed step-by-step instructions. Understand the key algebraic concepts and rules for solving inequalities. Suitable for students in Grades 7-9.

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