Solve 5/12-(3/8-x)=-5/6

$$\frac { 5 } { 12 } - ( \frac { 3 } { 8 } - x ) = - \frac { 5 } { 6 }$$

Solve for x

$$x=-\frac{7}{8}=-0.875$$

Steps for Solving Linear Equation

To find the opposite of \frac{3}{8}-x, find the opposite of each term.

$$\frac{5}{12}-\frac{3}{8}-\left(-x\right)=-\frac{5}{6}$$

The opposite of -x is x.

$$\frac{5}{12}-\frac{3}{8}+x=-\frac{5}{6}$$

Least common multiple of 12 and 8 is 24. Convert \frac{5}{12} and \frac{3}{8} to fractions with denominator 24.

$$\frac{10}{24}-\frac{9}{24}+x=-\frac{5}{6}$$

Since \frac{10}{24} and \frac{9}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-9}{24}+x=-\frac{5}{6}$$

Subtract 9 from 10 to get 1.

$$\frac{1}{24}+x=-\frac{5}{6}$$

Subtract \frac{1}{24} from both sides.

$$x=-\frac{5}{6}-\frac{1}{24}$$

Least common multiple of 6 and 24 is 24. Convert -\frac{5}{6} and \frac{1}{24} to fractions with denominator 24.

$$x=-\frac{20}{24}-\frac{1}{24}$$

Since -\frac{20}{24} and \frac{1}{24} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{-20-1}{24}$$

Subtract 1 from -20 to get -21.

$$x=\frac{-21}{24}$$

Reduce the fraction \frac{-21}{24} to lowest terms by extracting and canceling out 3.

$$x=-\frac{7}{8}$$