Solve for x 4(a+x)=b-a+2x

$4 (a + x) = b - a + 2 x$

Step 1

Simplify $4 (a + x)$ .

Rewrite.

$0 + 0 + 4 (a + x) = b - a + 2 x$

Simplify by adding zeros.

$4 (a + x) = b - a + 2 x$

Apply the distributive property.

$4 a + 4 x = b - a + 2 x$

Step 2

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

Subtract $2 x$ from both sides of the equation.

$4 a + 4 x - 2 x = b - a$

Subtract $2 x$ from $4 x$ .

$4 a + 2 x = b - a$

Step 3

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

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

$2 x = b - a - 4 a$

Subtract $4 a$ from $- a$ .

$2 x = b - 5 a$

Step 4

Divide each term in $2 x = b - 5 a$ by $2$ and simplify.

Divide each term in $2 x = b - 5 a$ by $2$ .

$\frac{2 x}{2} = \frac{b}{2} + \frac{- 5 a}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{b}{2} + \frac{- 5 a}{2}$

Divide $x$ by $1$ .

$x = \frac{b}{2} + \frac{- 5 a}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{b}{2} - \frac{5 a}{2}$