Solve -5/6-4/8x=-1/4x+4/3

$$- \frac { 5 } { 6 } - \frac { 4 } { 8 } x = - \frac { 1 } { 4 } x + \frac { 4 } { 3 }$$

Solve for x

$$x = -\frac{26}{3} = -8\frac{2}{3} \approx -8.666666667$$

Steps for Solving Linear Equation

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$-\frac{5}{6}-\frac{1}{2}x=-\frac{1}{4}x+\frac{4}{3}$$

Add \frac{1}{4}x to both sides.

$$-\frac{5}{6}-\frac{1}{2}x+\frac{1}{4}x=\frac{4}{3}$$

Combine -\frac{1}{2}x and \frac{1}{4}x to get -\frac{1}{4}x.

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

Add \frac{5}{6} to both sides.

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

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{5}{6} to fractions with denominator 6.

$$-\frac{1}{4}x=\frac{8}{6}+\frac{5}{6}$$

Since \frac{8}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$-\frac{1}{4}x=\frac{8+5}{6}$$

Add 8 and 5 to get 13.

$$-\frac{1}{4}x=\frac{13}{6}$$

Multiply both sides by -4, the reciprocal of -\frac{1}{4}.

$$x=\frac{13}{6}\left(-4\right)$$

Express \frac{13}{6}\left(-4\right) as a single fraction.

$$x=\frac{13\left(-4\right)}{6}$$

Multiply 13 and -4 to get -52.

$$x=\frac{-52}{6}$$

Reduce the fraction \frac{-52}{6} to lowest terms by extracting and canceling out 2.

$$x=-\frac{26}{3}$$