The problem is to solve for $x$ in the equation $\frac{4}{3}(x-1) = 4x - \frac{10}{3}$.

1. Problem Description

The problem is to solve for $x$ in the equation $\frac{4}{3}(x-1) = 4x - \frac{10}{3}$.

2. Solution Steps

First, distribute the $\frac{4}{3}$ on the left side of the equation:

$\frac{4}{3}x - \frac{4}{3} = 4x - \frac{10}{3}$

Next, multiply both sides of the equation by 3 to eliminate the fractions:

$3(\frac{4}{3}x - \frac{4}{3}) = 3(4x - \frac{10}{3})$

$4x - 4 = 12x - 10$

Now, subtract $4x$ from both sides:

$4x - 4 - 4x = 12x - 10 - 4x$

$-4 = 8x - 10$

Add 10 to both sides:

$-4 + 10 = 8x - 10 + 10$

$6 = 8x$

Finally, divide both sides by 8 to solve for $x$:

$\frac{6}{8} = \frac{8x}{8}$

$x = \frac{6}{8}$

Simplify the fraction:

$x = \frac{3}{4}$

3. Final Answer

$x = \frac{3}{4}$