We are given the equation:

\[
\frac{1}{3} \left( \frac{3}{4}f + 3 \right) - 2 = \frac{1}{2} \left( 2f - 4 \right)
\]

Let's solve it step by step.

### Step 1: Distribute terms on both sides
On the left-hand side, distribute \(\frac{1}{3}\) through the parentheses:
\[
\frac{1}{3} \times \frac{3}{4}f + \frac{1}{3} \times 3 = \frac{1}{2} \times (2f - 4)
\]

Simplifying:
\[
\frac{1}{4}f + 1 - 2 = f - 2
\]

### Step 2: Simplify both sides
Simplify the constants on the left side:
\[
\frac{1}{4}f - 1 = f - 2
\]

### Step 3: Eliminate fractions
To eliminate the fraction \(\frac{1}{4}f\), multiply the entire equation by 4:
\[
4 \times \left(\frac{1}{4}f - 1\right) = 4 \times \left(f - 2\right)
\]

Simplifying:
\[
f - 4 = 4f - 8
\]

### Step 4: Solve for \(f\)
Move all terms involving \(f\) to one side and constants to the other side:
\[
f - 4f = -8 + 4
\]
\[
-3f = -4
\]

Now, divide by \(-3\):
\[
f = \frac{-4}{-3} = \frac{4}{3}
\]

### Final answer:
\[
f = \frac{4}{3}
\]

Would you like further details or clarifications?

Here are 5 related questions to explore further:
1. How can we solve an equation with multiple fractions?
2. What happens when you multiply both sides of an equation by a fraction?
3. How do you simplify expressions with variables and constants?
4. What are the steps to isolate a variable in an equation?
5. Why is it important to check your solution in the original equation?

**Tip:** When solving equations with fractions, it's often helpful to eliminate fractions by multiplying through by a common denominator early on!

This guide walks through solving the linear equation 1/3(3/4f + 3) – 2 = 1/2(2f – 4) step by step. Learn how to distribute terms, simplify fractions, and isolate the variable. Suitable for students in Grades 8-10, covering key concepts like algebraic manipulation and fraction elimination.

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