To solve the inequality \( \frac{2z - 3}{4} > \frac{1}{4} \), follow these steps:

1. **Eliminate the denominator:** Multiply both sides of the inequality by 4 to get rid of the denominator:
   \[
   4 \times \frac{2z - 3}{4} > 4 \times \frac{1}{4}
   \]
   This simplifies to:
   \[
   2z - 3 > 1
   \]

2. **Isolate the variable:** Add 3 to both sides of the inequality to isolate the term with \( z \):
   \[
   2z > 1 + 3
   \]
   Simplifying further:
   \[
   2z > 4
   \]

3. **Solve for \( z \):** Divide both sides by 2:
   \[
   z > \frac{4}{2}
   \]
   Simplifying:
   \[
   z > 2
   \]

### Final Answer:
The solution to the inequality is \( z > 2 \).

Do you want more details or have any questions?

Here are 5 related questions:
1. How would the solution change if the inequality was \( \frac{2z - 3}{4} \geq \frac{1}{4} \)?
2. What is the solution if the inequality was \( \frac{3 - 2z}{4} > \frac{1}{4} \)?
3. How would you graph the solution \( z > 2 \) on a number line?
4. Can you solve \( \frac{2z - 3}{4} < -\frac{1}{4} \)?
5. What if the inequality was \( \frac{2z - 3}{4} = \frac{1}{4} \)? What is the value of \( z \)?

**Tip:** Always check your solution by plugging the value back into the original inequality to ensure it holds true.

This page provides a step-by-step solution to the inequality 2z - 3/4 > 1/4. The solution covers key algebraic concepts like linear inequalities and properties of inequalities. Ideal for students in Grades 7-8.

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