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

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

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

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

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

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

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

Add 3 and 2 to get 5.

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

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

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

Since \frac{5}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 5 to get 4.

$$x=\frac{4}{6}$$

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

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