Solve for x 3-2(x-2)=2-7x

$3 - 2 (x - 2) = 2 - 7 x$

Step 1

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

Simplify each term.

Apply the distributive property.

$3 - 2 x - 2 \cdot - 2 = 2 - 7 x$

Multiply $- 2$ by $- 2$ .

$3 - 2 x + 4 = 2 - 7 x$

Add $3$ and $4$ .

$- 2 x + 7 = 2 - 7 x$

Step 2

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

Add $7 x$ to both sides of the equation.

$- 2 x + 7 + 7 x = 2$

Add $- 2 x$ and $7 x$ .

$5 x + 7 = 2$

Step 3

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

Subtract $7$ from both sides of the equation.

$5 x = 2 - 7$

Subtract $7$ from $2$ .

$5 x = - 5$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 5$ by $5$ .

$x = - 1$