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

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Subtract x from both sides.

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

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

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

Add \frac{1}{6} to both sides.

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

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

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

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

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

Add 3 and 1 to get 4.

$$-\frac{1}{3}x=\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

$$x=\frac{2}{3}\left(-3\right)$$

Express \frac{2}{3}\left(-3\right) as a single fraction.

$$x=\frac{2\left(-3\right)}{3}$$

Multiply 2 and -3 to get -6.

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

Divide -6 by 3 to get -2.

$$x=-2$$