Solve -5/6x+3/4=1/3x-5/12

$$- \frac { 5 } { 6 } x + \frac { 3 } { 4 } = \frac { 1 } { 3 } x - \frac { 5 } { 12 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Subtract \frac{1}{3}x from both sides.

$$-\frac{5}{6}x+\frac{3}{4}-\frac{1}{3}x=-\frac{5}{12}$$

Combine -\frac{5}{6}x and -\frac{1}{3}x to get -\frac{7}{6}x.

$$-\frac{7}{6}x+\frac{3}{4}=-\frac{5}{12}$$

Subtract \frac{3}{4} from both sides.

$$-\frac{7}{6}x=-\frac{5}{12}-\frac{3}{4}$$

Least common multiple of 12 and 4 is 12. Convert -\frac{5}{12} and \frac{3}{4} to fractions with denominator 12.

$$-\frac{7}{6}x=-\frac{5}{12}-\frac{9}{12}$$

Since -\frac{5}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{7}{6}x=\frac{-5-9}{12}$$

Subtract 9 from -5 to get -14.

$$-\frac{7}{6}x=\frac{-14}{12}$$

Reduce the fraction \frac{-14}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{7}{6}x=-\frac{7}{6}$$

Multiply both sides by -\frac{6}{7}, the reciprocal of -\frac{7}{6}.

$$x=-\frac{7}{6}\left(-\frac{6}{7}\right)$$

Multiply -\frac{7}{6} times -\frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-7\left(-6\right)}{6\times 7}$$

Do the multiplications in the fraction \frac{-7\left(-6\right)}{6\times 7}.

$$x=\frac{42}{42}$$

Divide 42 by 42 to get 1.

$$x=1$$