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

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

Solve for x

$$x=\frac{3y+19}{2}$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Add 5 and \frac{4}{3} to get \frac{19}{3}.

$$\frac{2}{3}x=y+\frac{19}{3}$$

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

$$\frac{\frac{2}{3}x}{\frac{2}{3}}=\frac{y+\frac{19}{3}}{\frac{2}{3}}$$

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

$$x=\frac{y+\frac{19}{3}}{\frac{2}{3}}$$

Divide y+\frac{19}{3} by \frac{2}{3} by multiplying y+\frac{19}{3} by the reciprocal of \frac{2}{3}.

$$x=\frac{3y+19}{2}$$

Solve for y

$$y=\frac{2x-19}{3}$$

Solution Steps

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

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

Subtract 5 from both sides.

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

Subtract 5 from -\frac{4}{3} to get -\frac{19}{3}.

$$y=\frac{2}{3}x-\frac{19}{3}$$