Solve y-6=1/4(x+2)

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

Solve for x

$$x=4y-26$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{4} by x+2.

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

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

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

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

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

Subtract \frac{1}{2} from -6 to get -\frac{13}{2}.

$$\frac{1}{4}x=y-\frac{13}{2}$$

Multiply both sides by 4.

$$\frac{\frac{1}{4}x}{\frac{1}{4}}=\frac{y-\frac{13}{2}}{\frac{1}{4}}$$

Dividing by \frac{1}{4} undoes the multiplication by \frac{1}{4}.

$$x=\frac{y-\frac{13}{2}}{\frac{1}{4}}$$

Divide y-\frac{13}{2} by \frac{1}{4} by multiplying y-\frac{13}{2} by the reciprocal of \frac{1}{4}.

$$x=4y-26$$

Solve for y

$$y=\frac{x+26}{4}$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by x+2.

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

Add 6 to both sides.

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

Add \frac{1}{2} and 6 to get \frac{13}{2}.

$$y=\frac{1}{4}x+\frac{13}{2}$$