Solve for x (x-2)-2(x-1)=x+1-(x-4)

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

Step 1

Simplify $x - 2 - 2 (x - 1)$ .

Simplify each term.

Apply the distributive property.

$x - 2 - 2 x - 2 \cdot - 1 = x + 1 - (x - 4)$

Multiply $- 2$ by $- 1$ .

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

Simplify by adding terms.

Combine the opposite terms in $x - 2 - 2 x + 2$ .

Add $- 2$ and $2$ .

$x - 2 x + 0 = x + 1 - (x - 4)$

Add $x - 2 x$ and $0$ .

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

Subtract $2 x$ from $x$ .

$- x = x + 1 - (x - 4)$

Step 2

Simplify $x + 1 - (x - 4)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- 1$ by $- 4$ .

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

Simplify by adding terms.

Combine the opposite terms in $x + 1 - x + 4$ .

Subtract $x$ from $x$ .

$- x = 0 + 1 + 4$

Add $0$ and $1$ .

$- x = 1 + 4$

Add $1$ and $4$ .

$- x = 5$

Step 3

Divide each term in $- x = 5$ by $- 1$ and simplify.

Divide each term in $- x = 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{5}{- 1}$

Divide $x$ by $1$ .

$x = \frac{5}{- 1}$

Simplify the right side.

Divide $5$ by $- 1$ .

$x = - 5$