Solve y+6=-2/3(x+1)

$$y + 6 = - \frac { 2 } { 3 } ( x + 1 )$$

Solve for x

$$x=-\frac{3y}{2}-10$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{2}{3} by x+1.

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

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

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

Add \frac{2}{3} to both sides.

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

Add 6 and \frac{2}{3} to get \frac{20}{3}.

$$-\frac{2}{3}x=y+\frac{20}{3}$$

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

$$\frac{-\frac{2}{3}x}{-\frac{2}{3}}=\frac{y+\frac{20}{3}}{-\frac{2}{3}}$$

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

$$x=\frac{y+\frac{20}{3}}{-\frac{2}{3}}$$

Divide y+\frac{20}{3} by -\frac{2}{3} by multiplying y+\frac{20}{3} by the reciprocal of -\frac{2}{3}.

$$x=-\frac{3y}{2}-10$$

Solve for y

$$y=\frac{-2x-20}{3}$$

Solution Steps

Use the distributive property to multiply -\frac{2}{3} by x+1.

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

Subtract 6 from both sides.

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

Subtract 6 from -\frac{2}{3} to get -\frac{20}{3}.

$$y=-\frac{2}{3}x-\frac{20}{3}$$