Select the values that make the inequality w, ≤, 4w≤4 true.
(Numbers written in order from least to greatest going across.)

To solve the inequality \( w \leq 4w \leq 4 \), we'll break it down into two separate inequalities and solve each one.

### 1. Solve \( w \leq 4w \):
Subtract \( w \) from both sides:
\[
w - w \leq 4w - w
\]
\[
0 \leq 3w
\]
Divide both sides by 3:
\[
0 \leq w \quad \text{or} \quad w \geq 0
\]

### 2. Solve \( 4w \leq 4 \):
Divide both sides by 4:
\[
w \leq 1
\]

### Combine the results:
The values of \( w \) that satisfy both inequalities are those for which \( 0 \leq w \leq 1 \).

### Solution:
The inequality is true for \( w \) values in the interval \([0, 1]\).

So the answer is \( 0 \leq w \leq 1 \), or in interval notation, \( w \in [0, 1] \).

Would you like more details, or do you have any other questions? Here are some related questions:

1. What happens if the inequality changes to \( w \geq 4w \leq 4 \)?
2. How would the solution change if the inequality were strict, \( w < 4w < 4 \)?
3. What would the solution be if the inequality was \( w \leq 2w \leq 4 \)?
4. How do you solve inequalities involving absolute values?
5. Can you solve compound inequalities with more than three parts?

**Tip:** When solving compound inequalities, treat each part separately before combining the solutions.

Learn how to solve the inequality w ≤ 4w ≤ 4 with a detailed step-by-step solution. This problem covers key concepts in inequalities and algebraic manipulation. Suitable for high school students in Grades 9-12.

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