The problem is to solve the linear equation $2(x - 2) - (x - 1) = 2x - 2$ for $x$.

1. Problem Description

The problem is to solve the linear equation $2(x - 2) - (x - 1) = 2x - 2$ for $x$.

2. Solution Steps

First, distribute the $2$ in $2(x - 2)$:

$2(x - 2) = 2x - 4$

Next, distribute the negative sign in $-(x - 1)$:

$-(x - 1) = -x + 1$

Now, substitute these back into the original equation:

$2x - 4 - x + 1 = 2x - 2$

Combine like terms on the left side:

$2x - x - 4 + 1 = x - 3$

So the equation becomes:

$x - 3 = 2x - 2$

Subtract $x$ from both sides of the equation:

$x - 3 - x = 2x - 2 - x$

$-3 = x - 2$

Add $2$ to both sides of the equation:

$-3 + 2 = x - 2 + 2$

$-1 = x$

Thus, $x = -1$.

3. Final Answer

$x = -1$