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

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

Solve for x

$$x=\frac{3\left(y-6\right)}{2}$$

Steps for Solving Linear Equation

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

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

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

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

Subtract 2 from both sides.

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

Subtract 2 from -4 to get -6.

$$\frac{2}{3}x=y-6$$

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

$$\frac{\frac{2}{3}x}{\frac{2}{3}}=\frac{y-6}{\frac{2}{3}}$$

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

$$x=\frac{y-6}{\frac{2}{3}}$$

Divide y-6 by \frac{2}{3} by multiplying y-6 by the reciprocal of \frac{2}{3}.

$$x=\frac{3y}{2}-9$$

Solve for y

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

Solution Steps

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

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

Add 4 to both sides.

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

Add 2 and 4 to get 6.

$$y=\frac{2}{3}x+6$$