Solve for x 4(x-y)=2x+3

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

Step 1

Simplify $4 (x - y)$ .

Rewrite.

$0 + 0 + 4 (x - y) = 2 x + 3$

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $- 1$ by $4$ .

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

Step 2

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

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

$4 x - 4 y - 2 x = 3$

Subtract $2 x$ from $4 x$ .

$2 x - 4 y = 3$

Step 3

Add $4 y$ to both sides of the equation.

$2 x = 3 + 4 y$

Step 4

Divide each term in $2 x = 3 + 4 y$ by $2$ and simplify.

Divide each term in $2 x = 3 + 4 y$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2} + \frac{4 y}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2} + \frac{4 y}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2} + \frac{4 y}{2}$

Simplify the right side.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 y$ .

$x = \frac{3}{2} + \frac{2 (2 y)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = \frac{3}{2} + \frac{2 (2 y)}{2 (1)}$

Cancel the common factor.

$x = \frac{3}{2} + \frac{2 (2 y)}{2 \cdot 1}$

Rewrite the expression.

$x = \frac{3}{2} + \frac{2 y}{1}$

Divide $2 y$ by $1$ .

$x = \frac{3}{2} + 2 y$