Solve 1/2(x-3)-y-2x/2=x-1

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

Solve for x

$$x=y+1$$

Solution Steps

Multiply both sides of the equation by 2.

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

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

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

To find the opposite of y-2x, find the opposite of each term.

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

Combine x and 2x to get 3x.

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

Subtract 2x from both sides.

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

Combine 3x and -2x to get x.

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

Add 3 to both sides.

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

Add -2 and 3 to get 1.

$$x-y=1$$

Add y to both sides.

$$x=1+y$$

Solve for y

$$y=x-1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

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

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

To find the opposite of y-2x, find the opposite of each term.

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

Combine x and 2x to get 3x.

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

Subtract 3x from both sides.

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

Combine 2x and -3x to get -x.

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

Add 3 to both sides.

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

Add -2 and 3 to get 1.

$$-y=-x+1$$

The equation is in standard form.

$$-y=1-x$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{1-x}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{1-x}{-1}$$

Divide -x+1 by -1.

$$y=x-1$$