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

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

Solve for x

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

Steps for Solving Linear Equation

Subtract x from both sides.

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

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

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

Add \frac{1}{3} to both sides.

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

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

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

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

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

Add 3 and 2 to get 5.

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

Multiply both sides by -2, the reciprocal of -\frac{1}{2}.

$$x=\frac{5}{6}\left(-2\right)$$

Express \frac{5}{6}\left(-2\right) as a single fraction.

$$x=\frac{5\left(-2\right)}{6}$$

Multiply 5 and -2 to get -10.

$$x=\frac{-10}{6}$$

Reduce the fraction \frac{-10}{6} to lowest terms by extracting and canceling out 2.

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