Solve y(3-2x)-x=4(1-3x)+2

$$y ( 3 - 2 x ) - x = 4 ( 1 - 3 x ) + 2$$

Solve for x

$$x=-\frac{3\left(y-2\right)}{11-2y}$$

$$y\neq \frac{11}{2}$$

Steps for Solving Linear Equation

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

$$3y-2yx-x=4\left(1-3x\right)+2$$

Use the distributive property to multiply 4 by 1-3x.

$$3y-2yx-x=4-12x+2$$

Add 4 and 2 to get 6.

$$3y-2yx-x=6-12x$$

Add 12x to both sides.

$$3y-2yx-x+12x=6$$

Combine -x and 12x to get 11x.

$$3y-2yx+11x=6$$

Subtract 3y from both sides.

$$-2yx+11x=6-3y$$

Combine all terms containing x.

$$\left(-2y+11\right)x=6-3y$$

The equation is in standard form.

$$\left(11-2y\right)x=6-3y$$

Divide both sides by -2y+11.

$$\frac{\left(11-2y\right)x}{11-2y}=\frac{6-3y}{11-2y}$$

Dividing by -2y+11 undoes the multiplication by -2y+11.

$$x=\frac{6-3y}{11-2y}$$

Divide 6-3y by -2y+11.

$$x=\frac{3\left(2-y\right)}{11-2y}$$

Solve for y

$$y=-\frac{11x-6}{3-2x}$$

$$x\neq \frac{3}{2}$$

Steps for Solving Linear Equation

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

$$3y-2yx-x=4\left(1-3x\right)+2$$

Use the distributive property to multiply 4 by 1-3x.

$$3y-2yx-x=4-12x+2$$

Add 4 and 2 to get 6.

$$3y-2yx-x=6-12x$$

Add x to both sides.

$$3y-2yx=6-12x+x$$

Combine -12x and x to get -11x.

$$3y-2yx=6-11x$$

Combine all terms containing y.

$$\left(3-2x\right)y=6-11x$$

Divide both sides by 3-2x.

$$\frac{\left(3-2x\right)y}{3-2x}=\frac{6-11x}{3-2x}$$

Dividing by 3-2x undoes the multiplication by 3-2x.

$$y=\frac{6-11x}{3-2x}$$