Solve 1/6-3/2x=1/2-2/3x

$$\frac { 1 } { 6 } - \frac { 3 } { 2 } x = \frac { 1 } { 2 } - \frac { 2 } { 3 } x$$

Solve for x

$$x=-\frac{2}{5}=-0.4$$

Steps for Solving Linear Equation

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

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

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

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

Subtract \frac{1}{6} from both sides.

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

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{1}{6} to fractions with denominator 6.

$$-\frac{5}{6}x=\frac{3}{6}-\frac{1}{6}$$

Since \frac{3}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{6}x=\frac{3-1}{6}$$

Subtract 1 from 3 to get 2.

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

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{6}x=\frac{1}{3}$$

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

$$x=\frac{1}{3}\left(-\frac{6}{5}\right)$$

Multiply \frac{1}{3} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\left(-6\right)}{3\times 5}$$

Do the multiplications in the fraction \frac{1\left(-6\right)}{3\times 5}.

$$x=\frac{-6}{15}$$

Reduce the fraction \frac{-6}{15} to lowest terms by extracting and canceling out 3.

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