Solve 2x-3/4-1-3y/2=6y-1/2+3/4

$$\frac{ 2x-3 }{ 4 } - \frac{ 1-3y }{ 2 } = \frac{ 6y-1 }{ 2 } + \frac{ 3 }{ 4 }$$

Solve for x

$$x=3\left(y+1\right)$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$2x-3-2\left(1-3y\right)=2\left(6y-1\right)+3$$

Use the distributive property to multiply -2 by 1-3y.

$$2x-3-2+6y=2\left(6y-1\right)+3$$

Subtract 2 from -3 to get -5.

$$2x-5+6y=2\left(6y-1\right)+3$$

Use the distributive property to multiply 2 by 6y-1.

$$2x-5+6y=12y-2+3$$

Add -2 and 3 to get 1.

$$2x-5+6y=12y+1$$

Add 5 to both sides.

$$2x+6y=12y+1+5$$

Add 1 and 5 to get 6.

$$2x+6y=12y+6$$

Subtract 6y from both sides.

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

Combine 12y and -6y to get 6y.

$$2x=6y+6$$

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide 6+6y by 2.

$$x=3y+3$$

Solve for y

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$2x-3-2\left(1-3y\right)=2\left(6y-1\right)+3$$

Use the distributive property to multiply -2 by 1-3y.

$$2x-3-2+6y=2\left(6y-1\right)+3$$

Subtract 2 from -3 to get -5.

$$2x-5+6y=2\left(6y-1\right)+3$$

Use the distributive property to multiply 2 by 6y-1.

$$2x-5+6y=12y-2+3$$

Add -2 and 3 to get 1.

$$2x-5+6y=12y+1$$

Subtract 12y from both sides.

$$2x-5+6y-12y=1$$

Combine 6y and -12y to get -6y.

$$2x-5-6y=1$$

Subtract 2x from both sides.

$$-5-6y=1-2x$$

Add 5 to both sides.

$$-6y=1-2x+5$$

Add 1 and 5 to get 6.

$$-6y=6-2x$$

Divide both sides by -6.

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

Dividing by -6 undoes the multiplication by -6.

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

Divide 6-2x by -6.

$$y=\frac{x}{3}-1$$