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

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

Solve for y

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

Steps for Solving Linear Equation

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

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

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

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

Subtract \frac{1}{2} from both sides.

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

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

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

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

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

Divide x-\frac{1}{2} by \frac{3}{2} by multiplying x-\frac{1}{2} by the reciprocal of \frac{3}{2}.

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

Solve for x

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

Solution Steps

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

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