Solve 3/2x+1/2=2/3x-1/2

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

Solve for x

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

Steps for Solving Linear Equation

Subtract \frac{2}{3}x from both sides.

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

Combine \frac{3}{2}x and -\frac{2}{3}x to get \frac{5}{6}x.

$$\frac{5}{6}x+\frac{1}{2}=-\frac{1}{2}$$

Subtract \frac{1}{2} from both sides.

$$\frac{5}{6}x=-\frac{1}{2}-\frac{1}{2}$$

Since -\frac{1}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}x=\frac{-1-1}{2}$$

Subtract 1 from -1 to get -2.

$$\frac{5}{6}x=\frac{-2}{2}$$

Divide -2 by 2 to get -1.

$$\frac{5}{6}x=-1$$

Multiply both sides by \frac{6}{5}, the reciprocal of \frac{5}{6}.

$$x=-\frac{6}{5}$$