Solve y=2/3(p-2)+4

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

Solve for p

$$p=\frac{3y}{2}-4$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by p-2.

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

Add -\frac{4}{3} and 4 to get \frac{8}{3}.

$$y=\frac{2}{3}p+\frac{8}{3}$$

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

$$\frac{2}{3}p+\frac{8}{3}=y$$

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

$$\frac{2}{3}p=y-\frac{8}{3}$$

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

$$\frac{\frac{2}{3}p}{\frac{2}{3}}=\frac{y-\frac{8}{3}}{\frac{2}{3}}$$

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

$$p=\frac{y-\frac{8}{3}}{\frac{2}{3}}$$

Divide y-\frac{8}{3} by \frac{2}{3} by multiplying y-\frac{8}{3} by the reciprocal of \frac{2}{3}.

$$p=\frac{3y}{2}-4$$

Solve for y

$$y=\frac{2\left(p+4\right)}{3}$$

Solution Steps

Use the distributive property to multiply \frac{2}{3} by p-2.

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

Add -\frac{4}{3} and 4 to get \frac{8}{3}.

$$y=\frac{2}{3}p+\frac{8}{3}$$