https://file.aiquickdraw.com/mathbot/file/17298076370254dmgqtj4.jpg

Let's analyze the inequality from the image:

The inequality is:

\[
20 > \frac{30}{q} + 2
\]

We can solve for \( q \) step by step:

1. Subtract 2 from both sides:
   \[
   18 > \frac{30}{q}
   \]

2. Now, multiply both sides by \( q \) (assuming \( q > 0 \) because if \( q \) were negative, we'd flip the inequality):
   \[
   18q > 30
   \]

3. Divide both sides by 18:
   \[
   q > \frac{30}{18}
   \]

   Simplifying:
   \[
   q > \frac{5}{3}
   \]

So, the inequality is satisfied when \( q > \frac{5}{3} \), or approximately \( q > 1.67 \).

Let's check each option:

- \( q = 6 \): 
   \[
   20 > \frac{30}{6} + 2 \quad \text{(True, since } 20 > 7)
   \]

- \( q = 2 \): 
   \[
   20 > \frac{30}{2} + 2 \quad \text{(False, since } 20 > 17 \text{ is not true})
   \]

- \( q = 3 \): 
   \[
   20 > \frac{30}{3} + 2 \quad \text{(True, since } 20 > 12)
   \]

- \( q = 5 \):
   \[
   20 > \frac{30}{5} + 2 \quad \text{(True, since } 20 > 8)
   \]

Thus, the correct answers are \( q = 6 \), \( q = 3 \), and \( q = 5 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How does multiplying both sides by a variable affect an inequality?
2. What happens to the inequality if \( q \) were negative?
3. How would you graph this inequality on a number line?
4. How would the steps change if the inequality were \( 20 < \frac{30}{q} + 2 \)?
5. How can you verify inequality solutions using substitution?

**Tip**: Always remember to reverse the inequality sign if you multiply or divide by a negative number!

Which of the following are solutions to the inequality 20 > (30/q) + 2?

Learn how to solve the inequality 20 > (30/q) + 2, including step-by-step solutions for values of q. This problem covers key algebraic concepts like solving inequalities and inverse operations. Suitable for students in Grades 7-9.

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