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.