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

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

Solve for x

$$x=2y-\frac{11}{2}$$

Steps for Solving Linear Equation

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

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

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

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

Add \frac{1}{4} to both sides.

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

Add -3 and \frac{1}{4} to get -\frac{11}{4}.

$$\frac{1}{2}x=y-\frac{11}{4}$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}x}{\frac{1}{2}}=\frac{y-\frac{11}{4}}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$x=\frac{y-\frac{11}{4}}{\frac{1}{2}}$$

Divide y-\frac{11}{4} by \frac{1}{2} by multiplying y-\frac{11}{4} by the reciprocal of \frac{1}{2}.

$$x=2y-\frac{11}{2}$$

Solve for y

$$y=\frac{x}{2}+\frac{11}{4}$$

Solution Steps

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

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

Add 3 to both sides.

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

Add -\frac{1}{4} and 3 to get \frac{11}{4}.

$$y=\frac{1}{2}x+\frac{11}{4}$$