To solve the equation $\frac{2}{3}(x - 3) = \frac{x}{4}$, follow these steps:

Step 1: Eliminate the fractions

Multiply both sides of the equation by the least common denominator (LCD) of 3 and 4, which is 12, to get rid of the fractions.

$12 \times \frac{2}{3}(x - 3) = 12 \times \frac{x}{4}$

This simplifies to:

$4 \times 2(x - 3) = 3x$

$8(x - 3) = 3x$

Step 2: Distribute

Now distribute the 8 on the left-hand side:

$8x - 24 = 3x$

Step 3: Move all terms involving $x$ to one side

Subtract $3x$ from both sides:

$8x - 3x - 24 = 0$

This simplifies to:

$5x - 24 = 0$

Step 4: Solve for $x$

Add 24 to both sides:

$5x = 24$

Now, divide by 5:

$x = \frac{24}{5}$

So, the solution is:

$x = \frac{24}{5} \quad \text{or} \quad x = 4.8$

Would you like further details or have any questions?

Related Questions:

1. How do you solve equations with multiple fractions?
2. What is the least common denominator and how is it used in equations?
3. How do you check if your solution is correct in equations like this?
4. What are the steps to solve linear equations with distribution?
5. How would you handle this equation if there were more terms on either side?

Tip: Always double-check your solution by substituting it back into the original equation!