Solve for x 5x-(7x-4)-2=5-(3x+2)

$5 x - (7 x - 4) - 2 = 5 - (3 x + 2)$

Step 1

Simplify $5 x - (7 x - 4) - 2$ .

Simplify each term.

Apply the distributive property.

$5 x - (7 x) - - 4 - 2 = 5 - (3 x + 2)$

Multiply $7$ by $- 1$ .

$5 x - 7 x - - 4 - 2 = 5 - (3 x + 2)$

Multiply $- 1$ by $- 4$ .

$5 x - 7 x + 4 - 2 = 5 - (3 x + 2)$

Simplify by adding terms.

Subtract $7 x$ from $5 x$ .

$- 2 x + 4 - 2 = 5 - (3 x + 2)$

Subtract $2$ from $4$ .

$- 2 x + 2 = 5 - (3 x + 2)$

Step 2

Simplify $5 - (3 x + 2)$ .

Simplify each term.

Apply the distributive property.

$- 2 x + 2 = 5 - (3 x) - 1 \cdot 2$

Multiply $3$ by $- 1$ .

$- 2 x + 2 = 5 - 3 x - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$- 2 x + 2 = 5 - 3 x - 2$

Subtract $2$ from $5$ .

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

Step 3

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

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

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

Add $- 2 x$ and $3 x$ .

$x + 2 = 3$

Step 4

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

Subtract $2$ from both sides of the equation.

$x = 3 - 2$

Subtract $2$ from $3$ .

$x = 1$