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

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

Solve for x

$$x=\frac{1-2y}{15}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by \frac{1}{2}y-3x.

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

Use the distributive property to multiply \frac{1}{2} by 3x-1.

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

Subtract \frac{3}{2}x from both sides.

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

Combine -6x and -\frac{3}{2}x to get -\frac{15}{2}x.

$$y-\frac{15}{2}x=2y-\frac{1}{2}$$

Subtract y from both sides.

$$-\frac{15}{2}x=2y-\frac{1}{2}-y$$

Combine 2y and -y to get y.

$$-\frac{15}{2}x=y-\frac{1}{2}$$

Divide both sides of the equation by -\frac{15}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{15}{2}x}{-\frac{15}{2}}=\frac{y-\frac{1}{2}}{-\frac{15}{2}}$$

Dividing by -\frac{15}{2} undoes the multiplication by -\frac{15}{2}.

$$x=\frac{y-\frac{1}{2}}{-\frac{15}{2}}$$

Divide y-\frac{1}{2} by -\frac{15}{2} by multiplying y-\frac{1}{2} by the reciprocal of -\frac{15}{2}.

$$x=\frac{1-2y}{15}$$

Solve for y

$$y=\frac{1-15x}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by \frac{1}{2}y-3x.

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

Use the distributive property to multiply \frac{1}{2} by 3x-1.

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

Subtract 2y from both sides.

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

Combine y and -2y to get -y.

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

Add 6x to both sides.

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

Combine \frac{3}{2}x and 6x to get \frac{15}{2}x.

$$-y=\frac{15}{2}x-\frac{1}{2}$$

The equation is in standard form.

$$-y=\frac{15x-1}{2}$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{15x-1}{-2}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{15x-1}{-2}$$

Divide \frac{15x-1}{2} by -1.

$$y=\frac{1-15x}{2}$$