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

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

Solve for x

$$x=-\frac{1}{5}=-0.2$$

Steps for Solving Linear Equation

Combine \frac{2}{3}x and -\frac{1}{2}x to get \frac{1}{6}x.

$$\frac{1}{6}x=x+\frac{1}{6}$$

Subtract x from both sides.

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

Combine \frac{1}{6}x and -x to get -\frac{5}{6}x.

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

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

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

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

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

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

$$x=\frac{-6}{30}$$

Reduce the fraction \frac{-6}{30} to lowest terms by extracting and canceling out 6.

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