Solve y-1/2=(1/2+1/-4-frac{1{2}})(x+4)

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

Solve for x

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

Steps for Solving Linear Equation

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

$$y-\frac{1}{2}=\frac{\frac{3}{2}}{-4-\frac{1}{2}}\left(x+4\right)$$

Subtract \frac{1}{2} from -4 to get -\frac{9}{2}.

$$y-\frac{1}{2}=\frac{\frac{3}{2}}{-\frac{9}{2}}\left(x+4\right)$$

Divide \frac{3}{2} by -\frac{9}{2} by multiplying \frac{3}{2} by the reciprocal of -\frac{9}{2}.

$$y-\frac{1}{2}=\frac{3}{2}\left(-\frac{2}{9}\right)\left(x+4\right)$$

Multiply \frac{3}{2} and -\frac{2}{9} to get -\frac{1}{3}.

$$y-\frac{1}{2}=-\frac{1}{3}\left(x+4\right)$$

Use the distributive property to multiply -\frac{1}{3} by x+4.

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

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

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

Add \frac{4}{3} to both sides.

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

Add -\frac{1}{2} and \frac{4}{3} to get \frac{5}{6}.

$$-\frac{1}{3}x=y+\frac{5}{6}$$

Multiply both sides by -3.

$$\frac{-\frac{1}{3}x}{-\frac{1}{3}}=\frac{y+\frac{5}{6}}{-\frac{1}{3}}$$

Dividing by -\frac{1}{3} undoes the multiplication by -\frac{1}{3}.

$$x=\frac{y+\frac{5}{6}}{-\frac{1}{3}}$$

Divide y+\frac{5}{6} by -\frac{1}{3} by multiplying y+\frac{5}{6} by the reciprocal of -\frac{1}{3}.

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

Solve for y

$$y=-\frac{x}{3}-\frac{5}{6}$$

Solution Steps

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

$$y-\frac{1}{2}=\frac{\frac{3}{2}}{-4-\frac{1}{2}}\left(x+4\right)$$

Subtract \frac{1}{2} from -4 to get -\frac{9}{2}.

$$y-\frac{1}{2}=\frac{\frac{3}{2}}{-\frac{9}{2}}\left(x+4\right)$$

Divide \frac{3}{2} by -\frac{9}{2} by multiplying \frac{3}{2} by the reciprocal of -\frac{9}{2}.

$$y-\frac{1}{2}=\frac{3}{2}\left(-\frac{2}{9}\right)\left(x+4\right)$$

Multiply \frac{3}{2} and -\frac{2}{9} to get -\frac{1}{3}.

$$y-\frac{1}{2}=-\frac{1}{3}\left(x+4\right)$$

Use the distributive property to multiply -\frac{1}{3} by x+4.

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

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

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

Add -\frac{4}{3} and \frac{1}{2} to get -\frac{5}{6}.

$$y=-\frac{1}{3}x-\frac{5}{6}$$