https://file.aiquickdraw.com/mathbot/file/1724824751675uc9d0i2w.jpg

Let's solve the equation shown in the image. The equation is:

\[
\frac{3}{4}x - \frac{1}{2} = \frac{1}{3}x + 2
\]

### Step 1: Eliminate the fractions by finding a common denominator.
The least common multiple (LCM) of 4, 2, and 3 is 12. Multiply every term in the equation by 12 to eliminate the fractions:

\[
12 \times \left(\frac{3}{4}x\right) - 12 \times \left(\frac{1}{2}\right) = 12 \times \left(\frac{1}{3}x\right) + 12 \times 2
\]

### Step 2: Simplify each term.

\[
9x - 6 = 4x + 24
\]

### Step 3: Move the terms involving \(x\) to one side and constant terms to the other side.

Subtract \(4x\) from both sides:

\[
9x - 4x - 6 = 24
\]

\[
5x - 6 = 24
\]

### Step 4: Isolate \(x\).

Add 6 to both sides:

\[
5x = 30
\]

Divide by 5:

\[
x = 6
\]

### Solution:
The value of \(x\) is \( \boxed{6} \).

Would you like any further details or have any questions about this solution?

Here are five related questions to deepen your understanding:

1. How would the solution change if the constant term on the right side was different?
2. Can you solve the equation using a different method, such as graphing?
3. What happens if you multiply each term by a different common multiple?
4. How would you check if \(x = 6\) is indeed the correct solution?
5. What if the fractions had different numerators and denominators, how would that affect the process?

**Tip:** When solving equations with fractions, multiplying by the least common multiple can simplify the equation and make it easier to solve.

Learn how to solve an equation involving fractions with a detailed step-by-step guide. This problem covers key algebraic concepts and fractions. Suitable for students in Grades 7-9.

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