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

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

Solve for x

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

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.

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

Add 2 to both sides.

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

Add -4 and 2 to get -2.

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

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

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

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

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

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

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

Solve for y

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

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 2.

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