Let's solve the equation \( \frac{3}{4}(6x + 4) = 2x - 3 \).

### Step 1: Distribute the \( \frac{3}{4} \) on the left-hand side
\[
\frac{3}{4}(6x + 4) = \frac{3}{4} \cdot 6x + \frac{3}{4} \cdot 4
\]
Simplifying each term:
\[
\frac{3}{4} \cdot 6x = \frac{18x}{4} = 4.5x, \quad \frac{3}{4} \cdot 4 = 3
\]
Thus, the equation becomes:
\[
4.5x + 3 = 2x - 3
\]

### Step 2: Move the terms involving \(x\) to one side
Subtract \(2x\) from both sides:
\[
4.5x - 2x + 3 = -3
\]
Simplifying:
\[
2.5x + 3 = -3
\]

### Step 3: Isolate the \(x\)-term
Subtract 3 from both sides:
\[
2.5x = -6
\]

### Step 4: Solve for \(x\)
Divide both sides by 2.5:
\[
x = \frac{-6}{2.5} = -2.4
\]

### Final Answer:
\[
x = -2.4
\]

Would you like any more details on this solution? 

Here are some related questions to explore:
1. How do you solve other types of linear equations?
2. What happens if you have fractions on both sides of the equation?
3. How do you check if a solution is correct?
4. What if the equation had no solution? How would you know?
5. How would you solve this problem if it were written in a different form?

**Tip:** Always check your solution by substituting it back into the original equation.

Explore the step-by-step process of solving the linear equation 3/4(6x + 4) = 2x - 3. This tutorial covers key algebraic concepts, including the distributive property and solving equations with fractions, making it suitable for students in Grades 8-10.

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