Solve y-5=4/3(x+2)

$$y - 5 = \frac { 4 } { 3 } ( x + 2 )$$

Solve for x

$$x=\frac{3y-23}{4}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{4}{3} by x+2.

$$y-5=\frac{4}{3}x+\frac{8}{3}$$

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

$$\frac{4}{3}x+\frac{8}{3}=y-5$$

Subtract \frac{8}{3} from both sides.

$$\frac{4}{3}x=y-5-\frac{8}{3}$$

Subtract \frac{8}{3} from -5 to get -\frac{23}{3}.

$$\frac{4}{3}x=y-\frac{23}{3}$$

Divide both sides of the equation by \frac{4}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{4}{3}x}{\frac{4}{3}}=\frac{y-\frac{23}{3}}{\frac{4}{3}}$$

Dividing by \frac{4}{3} undoes the multiplication by \frac{4}{3}.

$$x=\frac{y-\frac{23}{3}}{\frac{4}{3}}$$

Divide y-\frac{23}{3} by \frac{4}{3} by multiplying y-\frac{23}{3} by the reciprocal of \frac{4}{3}.

$$x=\frac{3y-23}{4}$$

Solve for y

$$y=\frac{4x+23}{3}$$

Solution Steps

Use the distributive property to multiply \frac{4}{3} by x+2.

$$y-5=\frac{4}{3}x+\frac{8}{3}$$

Add 5 to both sides.

$$y=\frac{4}{3}x+\frac{8}{3}+5$$

Add \frac{8}{3} and 5 to get \frac{23}{3}.

$$y=\frac{4}{3}x+\frac{23}{3}$$