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

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

Solve for x

$$x=\frac{2y+5}{3}$$

Steps for Solving Linear Equation

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

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

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

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

Add 3 to both sides.

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

Add -\frac{1}{2} and 3 to get \frac{5}{2}.

$$\frac{3}{2}x=y+\frac{5}{2}$$

Divide both sides of the equation by \frac{3}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{3}{2}x}{\frac{3}{2}}=\frac{y+\frac{5}{2}}{\frac{3}{2}}$$

Dividing by \frac{3}{2} undoes the multiplication by \frac{3}{2}.

$$x=\frac{y+\frac{5}{2}}{\frac{3}{2}}$$

Divide y+\frac{5}{2} by \frac{3}{2} by multiplying y+\frac{5}{2} by the reciprocal of \frac{3}{2}.

$$x=\frac{2y+5}{3}$$

Solve for y

$$y=\frac{3x-5}{2}$$

Solution Steps

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

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

Add \frac{1}{2} to both sides.

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

Add -3 and \frac{1}{2} to get -\frac{5}{2}.

$$y=\frac{3}{2}x-\frac{5}{2}$$