Solve 5/6-1/3x=5/12

$$\frac { 5 } { 6 } - \frac { 1 } { 3 } x = \frac { 5 } { 12 }$$

Solve for x

$$x = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

Steps for Solving Linear Equation

Subtract \frac{5}{6} from both sides.

$$-\frac{1}{3}x=\frac{5}{12}-\frac{5}{6}$$

Least common multiple of 12 and 6 is 12. Convert \frac{5}{12} and \frac{5}{6} to fractions with denominator 12.

$$-\frac{1}{3}x=\frac{5}{12}-\frac{10}{12}$$

Since \frac{5}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}x=\frac{5-10}{12}$$

Subtract 10 from 5 to get -5.

$$-\frac{1}{3}x=-\frac{5}{12}$$

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

$$x=-\frac{5}{12}\left(-3\right)$$

Express -\frac{5}{12}\left(-3\right) as a single fraction.

$$x=\frac{-5\left(-3\right)}{12}$$

Multiply -5 and -3 to get 15.

$$x=\frac{15}{12}$$

Reduce the fraction \frac{15}{12} to lowest terms by extracting and canceling out 3.

$$x=\frac{5}{4}$$