The problem asks us to solve the equation $4x = x - (x - 2)$ for $x$.

1. Problem Description

The problem asks us to solve the equation $4x = x - (x - 2)$ for $x$.

2. Solution Steps

First, simplify the right side of the equation by distributing the negative sign:

$4x = x - x + 2$

Next, simplify the right side further by combining like terms:

$4x = 0 + 2$

$4x = 2$

Now, divide both sides of the equation by 4 to isolate $x$:

$\frac{4x}{4} = \frac{2}{4}$

$x = \frac{1}{2}$

3. Final Answer

$x = \frac{1}{2}$