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

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

Solve for x

$$x=\frac{1-2y}{3}$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Add -2 and \frac{3}{2} to get -\frac{1}{2}.

$$-\frac{3}{2}x=y-\frac{1}{2}$$

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

$$\frac{-\frac{3}{2}x}{-\frac{3}{2}}=\frac{y-\frac{1}{2}}{-\frac{3}{2}}$$

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

$$x=\frac{y-\frac{1}{2}}{-\frac{3}{2}}$$

Divide y-\frac{1}{2} by -\frac{3}{2} by multiplying y-\frac{1}{2} by the reciprocal of -\frac{3}{2}.

$$x=\frac{1-2y}{3}$$

Solve for y

$$y=\frac{1-3x}{2}$$

Solution Steps

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

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

Add 2 to both sides.

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

Add -\frac{3}{2} and 2 to get \frac{1}{2}.

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