Evaluate 2(x+1)-3(x-2)=x+6

$2 (x + 1) - 3 (x - 2) = x + 6$

Simplify $2 (x + 1) - 3 (x - 2)$ .

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot 1 - 3 (x - 2) = x + 6$

Multiply $2$ by $1$ .

$2 x + 2 - 3 (x - 2) = x + 6$

Apply the distributive property.

$2 x + 2 - 3 x - 3 \cdot - 2 = x + 6$

Multiply $- 3$ by $- 2$ .

$2 x + 2 - 3 x + 6 = x + 6$

Simplify by adding terms.

Subtract $3 x$ from $2 x$ .

$- x + 2 + 6 = x + 6$

Add $2$ and $6$ .

$- x + 8 = x + 6$

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

Subtract $x$ from both sides of the equation.

$- x + 8 - x = 6$

Subtract $x$ from $- x$ .

$- 2 x + 8 = 6$

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

Subtract $8$ from both sides of the equation.

$- 2 x = 6 - 8$

Subtract $8$ from $6$ .

$- 2 x = - 2$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 2$ by $- 2$ .

$x = 1$