Solve 2-y+2x/10+1/5x=12/5(1-x/4)

$$2 - \frac { y + 2 x } { 10 } + \frac { 1 } { 5 } x = \frac { 12 } { 5 } ( 1 - \frac { x } { 4 } )$$

Solve for x

$$x=\frac{y+4}{6}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 10,5,4.

$$40-2\left(y+2x\right)+4x=48\left(1-\frac{x}{4}\right)$$

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

$$40-2y-4x+4x=48\left(1-\frac{x}{4}\right)$$

Combine -4x and 4x to get 0.

$$40-2y=48\left(1-\frac{x}{4}\right)$$

Use the distributive property to multiply 48 by 1-\frac{x}{4}.

$$40-2y=48+48\left(-\frac{x}{4}\right)$$

Cancel out 4, the greatest common factor in 48 and 4.

$$40-2y=48-12x$$

Swap sides so that all variable terms are on the left hand side.

$$48-12x=40-2y$$

Subtract 48 from both sides.

$$-12x=40-2y-48$$

Subtract 48 from 40 to get -8.

$$-12x=-8-2y$$

The equation is in standard form.

$$-12x=-2y-8$$

Divide both sides by -12.

$$\frac{-12x}{-12}=\frac{-2y-8}{-12}$$

Dividing by -12 undoes the multiplication by -12.

$$x=\frac{-2y-8}{-12}$$

Divide -8-2y by -12.

$$x=\frac{y}{6}+\frac{2}{3}$$

Solve for y

$$y=6x-4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 10,5,4.

$$40-2\left(y+2x\right)+4x=48\left(1-\frac{x}{4}\right)$$

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

$$40-2y-4x+4x=48\left(1-\frac{x}{4}\right)$$

Combine -4x and 4x to get 0.

$$40-2y=48\left(1-\frac{x}{4}\right)$$

Use the distributive property to multiply 48 by 1-\frac{x}{4}.

$$40-2y=48+48\left(-\frac{x}{4}\right)$$

Cancel out 4, the greatest common factor in 48 and 4.

$$40-2y=48-12x$$

Subtract 40 from both sides.

$$-2y=48-12x-40$$

Subtract 40 from 48 to get 8.

$$-2y=8-12x$$

Divide both sides by -2.

$$\frac{-2y}{-2}=\frac{8-12x}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$y=\frac{8-12x}{-2}$$

Divide 8-12x by -2.

$$y=6x-4$$