We need to solve the equation $3x - \frac{2}{3}(2x-1) = 4$ for $x$.

1. Problem Description

We need to solve the equation $3x - \frac{2}{3}(2x-1) = 4$ for $x$.

2. Solution Steps

First, distribute the $-\frac{2}{3}$ to the terms inside the parentheses:

$3x - \frac{2}{3}(2x) - \frac{2}{3}(-1) = 4$

$3x - \frac{4}{3}x + \frac{2}{3} = 4$

Next, we need to combine the terms with $x$. To do this, we need a common denominator, which is

3. $\frac{9}{3}x - \frac{4}{3}x + \frac{2}{3} = 4$

$\frac{5}{3}x + \frac{2}{3} = 4$

Subtract $\frac{2}{3}$ from both sides of the equation:

$\frac{5}{3}x = 4 - \frac{2}{3}$

$\frac{5}{3}x = \frac{12}{3} - \frac{2}{3}$

$\frac{5}{3}x = \frac{10}{3}$

Now, multiply both sides of the equation by $\frac{3}{5}$ to isolate $x$:

$x = \frac{10}{3} \cdot \frac{3}{5}$

$x = \frac{10 \cdot 3}{3 \cdot 5}$

$x = \frac{30}{15}$

$x = 2$

3. Final Answer

The solution is $x = 2$.