https://file.aiquickdraw.com/mathbot/file/1727742994359cceemxhx.jpg

The inequality shown in the image is:

\[
31 > \frac{u}{4}
\]

To solve for \( u \), let's manipulate the inequality step by step.

1. Multiply both sides by 4 to eliminate the fraction:
   \[
   31 \times 4 > u
   \]
   \[
   124 > u
   \]
   This simplifies to:
   \[
   u < 124
   \]

So, the solutions for \( u \) must be values less than 124.

Now, let's evaluate the given options:
- \( u = 52 \): \( 52 < 124 \), so this is a solution.
- \( u = 132 \): \( 132 > 124 \), so this is **not** a solution.
- \( u = 84 \): \( 84 < 124 \), so this is a solution.
- \( u = 88 \): \( 88 < 124 \), so this is a solution.

Therefore, the correct solutions are \( u = 52 \), \( u = 84 \), and \( u = 88 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do we solve inequalities with fractions?
2. What happens when you multiply or divide both sides of an inequality by a negative number?
3. Can you explain how to check solutions for inequalities?
4. How do inequalities differ from equations in terms of solutions?
5. What is the process to graph a solution of an inequality on a number line?

**Tip:** Always remember that multiplying or dividing by a negative number reverses the inequality sign.

Which of the following are solutions to the inequality 31 > u/4?

Discover how to solve the inequality 31 > u/4 by applying algebraic concepts. Learn how to eliminate fractions by multiplying both sides and check which values of u satisfy the inequality. This problem is suitable for Grade 8 students.

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