Solve for x 2(x-a)+b=3x+a

$2 (x - a) + b = 3 x + a$

Step 1

Simplify each term.

Apply the distributive property.

$2 x + 2 (- a) + b = 3 x + a$

Multiply $- 1$ by $2$ .

$2 x - 2 a + b = 3 x + a$

Step 2

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

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

$2 x - 2 a + b - 3 x = a$

Subtract $3 x$ from $2 x$ .

$- 2 a + b - x = a$

Step 3

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

Add $2 a$ to both sides of the equation.

$b - x = a + 2 a$

Subtract $b$ from both sides of the equation.

$- x = a + 2 a - b$

Add $a$ and $2 a$ .

$- x = 3 a - b$

Step 4

Divide each term in $- x = 3 a - b$ by $- 1$ and simplify.

Divide each term in $- x = 3 a - b$ by $- 1$ .

$\frac{- x}{- 1} = \frac{3 a}{- 1} + \frac{- b}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{3 a}{- 1} + \frac{- b}{- 1}$

Divide $x$ by $1$ .

$x = \frac{3 a}{- 1} + \frac{- b}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{3 a}{- 1}$ .

$x = - 1 \cdot (3 a) + \frac{- b}{- 1}$

Rewrite $- 1 \cdot (3 a)$ as $- (3 a)$ .

$x = - (3 a) + \frac{- b}{- 1}$

Multiply $3$ by $- 1$ .

$x = - 3 a + \frac{- b}{- 1}$

Dividing two negative values results in a positive value.

$x = - 3 a + \frac{b}{1}$

Divide $b$ by $1$ .

$x = - 3 a + b$