Solve x-y/3+3-x/12=x-2y/4

$$\frac { x - y } { 3 } + \frac { 3 - x } { 12 } = \frac { x - 2 y } { 4 }$$

Solve for y

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,12,4.

$$4\left(x-y\right)+3-x=3\left(x-2y\right)$$

Use the distributive property to multiply 4 by x-y.

$$4x-4y+3-x=3\left(x-2y\right)$$

Combine 4x and -x to get 3x.

$$3x-4y+3=3\left(x-2y\right)$$

Use the distributive property to multiply 3 by x-2y.

$$3x-4y+3=3x-6y$$

Add 6y to both sides.

$$3x-4y+3+6y=3x$$

Combine -4y and 6y to get 2y.

$$3x+2y+3=3x$$

Subtract 3x from both sides.

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

Combine 3x and -3x to get 0.

$$2y+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$2y=-3$$

Divide both sides by 2.

$$y=\frac{-3}{2}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$y=-\frac{3}{2}$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Solve for x

$$x\in \mathrm{R}$$

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$