https://file.aiquickdraw.com/mathbot/file/1727087523983s47kq5p9.jpg

The inequality shown in the image is:

\[
\frac{-3}{4}q + \frac{7}{4} > 3q
\]

### Step-by-step solution:

1. **Multiply through by 4** to eliminate the fractions:
   \[
   -3q + 7 > 12q
   \]

2. **Move all terms involving \( q \) to one side** by adding \( 3q \) to both sides:
   \[
   7 > 15q
   \]

3. **Isolate \( q \)** by dividing both sides by 15:
   \[
   \frac{7}{15} > q
   \]

Or equivalently:
\[
q < \frac{7}{15}
\]

### Solution:
The solution to the inequality is \( q < \frac{7}{15} \).

Would you like any further details or explanations?

Here are five related questions for practice:
1. Solve the inequality \( \frac{5}{2}q + \frac{1}{4} > 4q \).
2. What happens to the inequality sign when you multiply or divide by a negative number?
3. Solve \( 2x - \frac{3}{5} > 1 + \frac{2}{3}x \).
4. How do you solve a system of linear inequalities?
5. What is the geometric interpretation of an inequality like this?

**Tip:** Always be careful when multiplying or dividing both sides of an inequality by a negative number. The inequality sign reverses in such cases.

Learn how to solve the linear inequality -(3/4)q + 7/4 > 3q using step-by-step algebraic methods. This solution covers key concepts like multiplying to eliminate fractions and solving inequalities. Perfect for students in Grades 8-10.

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