Solve for x 5x+2(1-x)=2(2x-1)

$5 x + 2 (1 - x) = 2 (2 x - 1)$

Simplify $5 x + 2 (1 - x)$ .

Simplify each term.

Apply the distributive property.

$5 x + 2 \cdot 1 + 2 (- x) = 2 (2 x - 1)$

Multiply $2$ by $1$ .

$5 x + 2 + 2 (- x) = 2 (2 x - 1)$

Multiply $- 1$ by $2$ .

$5 x + 2 - 2 x = 2 (2 x - 1)$

Subtract $2 x$ from $5 x$ .

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

Simplify $2 (2 x - 1)$ .

Apply the distributive property.

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

Multiply.

Multiply $2$ by $2$ .

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

Multiply $2$ by $- 1$ .

$3 x + 2 = 4 x - 2$

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

Subtract $4 x$ from both sides of the equation.

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

Subtract $4 x$ from $3 x$ .

$- x + 2 = - 2$

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

Subtract $2$ from both sides of the equation.

$- x = - 2 - 2$

Subtract $2$ from $- 2$ .

$- x = - 4$

Divide each term in $- x = - 4$ by $- 1$ and simplify.

Divide each term in $- x = - 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 4}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 1}$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$x = 4$