https://file.aiquickdraw.com/mathbot/file/1726704107612ziay43m4.jpg

Let's solve the inequality to determine which values of \( w \) satisfy it:

The given inequality is:

\[
29 > \frac{w}{4} + 2
\]

### Step 1: Subtract 2 from both sides
\[
29 - 2 > \frac{w}{4}
\]
\[
27 > \frac{w}{4}
\]

### Step 2: Multiply both sides by 4 to eliminate the denominator
\[
27 \times 4 > w
\]
\[
108 > w
\]
This simplifies to:
\[
w < 108
\]

### Step 3: Evaluate the given options
We now need to check which of the provided values for \( w \) are less than 108:

- \( w = 136 \) (This is not a solution because 136 is greater than 108)
- \( w = 20 \) (This is a solution because 20 is less than 108)
- \( w = 108 \) (This is not a solution because 108 is not less than 108)
- \( w = 120 \) (This is not a solution because 120 is greater than 108)

### Conclusion:
The correct solution from the options is **\( w = 20 \)**.

Would you like further details on how this inequality was solved, or do you have any additional questions?

Here are 5 questions related to inequalities and number properties:
1. How do you solve inequalities involving fractions?
2. What happens when you multiply or divide an inequality by a negative number?
3. Can you explain how to graph solutions of inequalities on a number line?
4. How do compound inequalities differ from simple inequalities?
5. How do you handle absolute value inequalities?

**Tip:** Always check the boundary condition (e.g., \( w = 108 \)) carefully when solving inequalities!

Which of the following are solutions to the inequality: 29 > w/4 + 2?

Learn how to solve the inequality 29 > w/4 + 2 with a step-by-step explanation. Check which values satisfy the inequality using basic algebraic methods. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation