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

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Multiply $5$ by $- 2$ .

$5 x - 10 + 2 x = 2 (x - 5) + x$

Add $5 x$ and $2 x$ .

$7 x - 10 = 2 (x - 5) + x$

Step 2

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

Simplify each term.

Apply the distributive property.

$7 x - 10 = 2 x + 2 \cdot - 5 + x$

Multiply $2$ by $- 5$ .

$7 x - 10 = 2 x - 10 + x$

Add $2 x$ and $x$ .

$7 x - 10 = 3 x - 10$

Step 3

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

Subtract $3 x$ from both sides of the equation.

$7 x - 10 - 3 x = - 10$

Subtract $3 x$ from $7 x$ .

$4 x - 10 = - 10$

Step 4

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

Add $10$ to both sides of the equation.

$4 x = - 10 + 10$

Add $- 10$ and $10$ .

$4 x = 0$

Step 5

Divide each term in $4 x = 0$ by $4$ and simplify.

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

Divide $x$ by $1$ .

$x = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x = 0$