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Let's solve the given compound inequality step by step.

### 1. The inequalities are:
- \( -3w \leq 12 \)
- \( 4w - 4 \geq 16 \)

These are connected by the word "or," meaning we need to solve each inequality independently, then combine the results using union (since "or" means either inequality can be satisfied).

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### 2. Solve the first inequality: \( -3w \leq 12 \)

Divide both sides by \(-3\). Remember to reverse the inequality sign when dividing by a negative number:
\[
w \geq -4
\]

### 3. Solve the second inequality: \( 4w - 4 \geq 16 \)

First, add 4 to both sides:
\[
4w \geq 20
\]
Next, divide by 4:
\[
w \geq 5
\]

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### 4. Combine the solutions:

The two inequalities are \( w \geq -4 \) and \( w \geq 5 \), connected by "or." The solution to the inequality will include all values of \(w\) where either inequality is satisfied.

For \( w \geq -4 \), the values start from \(-4\) and go to infinity. For \( w \geq 5 \), the values start from 5 and go to infinity. Since these two intervals overlap from \(5\) onwards, the overall solution will be:
\[
w \geq -4 \text{ or } w \geq 5
\]
This simplifies to:
\[
w \geq -4
\]

---

### 5. Write the solution in interval notation:

Since \( w \geq -4 \), the solution in interval notation is:
\[
[-4, \infty)
\]

Would you like more details or clarifications on any of the steps?

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Here are 5 related questions to expand on this concept:
1. How would the solution change if the inequalities were connected by "and" instead of "or"?
2. How do you solve a compound inequality involving three separate inequalities?
3. What is the significance of reversing the inequality when dividing by a negative number?
4. How do you graph inequalities on a number line?
5. How can compound inequalities be used to model real-world scenarios?

**Tip**: Always check whether you need to reverse the inequality sign when multiplying or dividing by a negative number!

Solve the compound inequality: -3w ≤ 12 or 4w - 4 ≥ 16. Write the solution in interval notation. If there is no solution, enter Ø.

Learn how to solve the compound inequality -3w ≤ 12 or 4w - 4 ≥ 16. This step-by-step guide explains the process of solving inequalities and combining them using interval notation. Ideal for students in Grades 8-10.

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