Solve 12/7+3/14-5/6x=128/14

$$\frac { 12 } { 7 } + \frac { 3 } { 14 } - \frac { 5 } { 6 } x = \frac { 128 } { 14 }$$

Solve for x

$$x = -\frac{303}{35} = -8\frac{23}{35} \approx -8.657142857$$

Steps for Solving Linear Equation

Least common multiple of 7 and 14 is 14. Convert \frac{12}{7} and \frac{3}{14} to fractions with denominator 14.

$$\frac{24}{14}+\frac{3}{14}-\frac{5}{6}x=\frac{128}{14}$$

Since \frac{24}{14} and \frac{3}{14} have the same denominator, add them by adding their numerators.

$$\frac{24+3}{14}-\frac{5}{6}x=\frac{128}{14}$$

Add 24 and 3 to get 27.

$$\frac{27}{14}-\frac{5}{6}x=\frac{128}{14}$$

Reduce the fraction \frac{128}{14} to lowest terms by extracting and canceling out 2.

$$\frac{27}{14}-\frac{5}{6}x=\frac{64}{7}$$

Subtract \frac{27}{14} from both sides.

$$-\frac{5}{6}x=\frac{64}{7}-\frac{27}{14}$$

Least common multiple of 7 and 14 is 14. Convert \frac{64}{7} and \frac{27}{14} to fractions with denominator 14.

$$-\frac{5}{6}x=\frac{128}{14}-\frac{27}{14}$$

Since \frac{128}{14} and \frac{27}{14} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{6}x=\frac{128-27}{14}$$

Subtract 27 from 128 to get 101.

$$-\frac{5}{6}x=\frac{101}{14}$$

Multiply both sides by -\frac{6}{5}, the reciprocal of -\frac{5}{6}.

$$x=\frac{101}{14}\left(-\frac{6}{5}\right)$$

Multiply \frac{101}{14} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{101\left(-6\right)}{14\times 5}$$

Do the multiplications in the fraction \frac{101\left(-6\right)}{14\times 5}.

$$x=\frac{-606}{70}$$

Reduce the fraction \frac{-606}{70} to lowest terms by extracting and canceling out 2.

$$x=-\frac{303}{35}$$