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

### Step 1: Cross-multiply
First, ensure that both sides of the inequality are positive. Assuming \(p-1 > 0\) (which implies \(p > 1\)), we can safely cross-multiply:

\[
4 \times 2 \geq 3 \times (p - 1)
\]

### Step 2: Simplify
Simplify both sides of the equation:

\[
8 \geq 3p - 3
\]

### Step 3: Solve for \(p\)
Add 3 to both sides to isolate the term involving \(p\):

\[
11 \geq 3p
\]

Now, divide both sides by 3:

\[
\frac{11}{3} \geq p \quad \text{or} \quad p \leq \frac{11}{3}
\]

### Step 4: Consider the Domain
Remember, \(p - 1 > 0\), so \(p > 1\). Thus, the solution for \(p\) must satisfy both \(p > 1\) and \(p \leq \frac{11}{3}\).

### Final Answer
The solution is:

\[
1 < p \leq \frac{11}{3}
\]

Would you like more details, or do you have any questions?

Here are five related questions you might be interested in:
1. How do you solve inequalities involving absolute values?
2. What is the process for solving quadratic inequalities?
3. How do you graph solutions to inequalities on a number line?
4. Can you explain how to solve systems of inequalities?
5. What are the common mistakes to avoid when solving inequalities?

**Tip:** When solving inequalities, always remember to consider the domain of the variable, especially when dealing with fractions or square roots.

Discover how to solve the inequality 2/(p-1) ≥ 3/4 step-by-step. This guide covers essential algebraic concepts, including cross-multiplication and properties of inequalities, perfect for students in Grades 7-9.

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