Solve for x -(x-1)+10=-3(x-2)

$- (x - 1) + 10 = - 3 (x - 2)$

Simplify $- (x - 1) + 10$ .

Simplify each term.

Apply the distributive property.

$- x - - 1 + 10 = - 3 (x - 2)$

Multiply $- 1$ by $- 1$ .

$- x + 1 + 10 = - 3 (x - 2)$

Add $1$ and $10$ .

$- x + 11 = - 3 (x - 2)$

Simplify $- 3 (x - 2)$ .

Apply the distributive property.

$- x + 11 = - 3 x - 3 \cdot - 2$

Multiply $- 3$ by $- 2$ .

$- x + 11 = - 3 x + 6$

Move all terms containing $x$ to the left side of the equation.

Add $3 x$ to both sides of the equation.

$- x + 11 + 3 x = 6$

Add $- x$ and $3 x$ .

$2 x + 11 = 6$

Move all terms not containing $x$ to the right side of the equation.

Subtract $11$ from both sides of the equation.

$2 x = 6 - 11$

Subtract $11$ from $6$ .

$2 x = - 5$

Divide each term in $2 x = - 5$ by $2$ and simplify.

Divide each term in $2 x = - 5$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 2.5$

Mixed Number Form:

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