Solve 1/6-3/7x=1/7-2/3x

$$\frac { 1 } { 6 } - \frac { 3 } { 7 } x = \frac { 1 } { 7 } - \frac { 2 } { 3 } x$$

Solve for x

$$x=-\frac{1}{10}=-0.1$$

Steps for Solving Linear Equation

Add \frac{2}{3}x to both sides.

$$\frac{1}{6}-\frac{3}{7}x+\frac{2}{3}x=\frac{1}{7}$$

Combine -\frac{3}{7}x and \frac{2}{3}x to get \frac{5}{21}x.

$$\frac{1}{6}+\frac{5}{21}x=\frac{1}{7}$$

Subtract \frac{1}{6} from both sides.

$$\frac{5}{21}x=\frac{1}{7}-\frac{1}{6}$$

Least common multiple of 7 and 6 is 42. Convert \frac{1}{7} and \frac{1}{6} to fractions with denominator 42.

$$\frac{5}{21}x=\frac{6}{42}-\frac{7}{42}$$

Since \frac{6}{42} and \frac{7}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{21}x=\frac{6-7}{42}$$

Subtract 7 from 6 to get -1.

$$\frac{5}{21}x=-\frac{1}{42}$$

Multiply both sides by \frac{21}{5}, the reciprocal of \frac{5}{21}.

$$x=-\frac{1}{42}\times \frac{21}{5}$$

Multiply -\frac{1}{42} times \frac{21}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-21}{42\times 5}$$

Do the multiplications in the fraction \frac{-21}{42\times 5}.

$$x=\frac{-21}{210}$$

Reduce the fraction \frac{-21}{210} to lowest terms by extracting and canceling out 21.

$$x=-\frac{1}{10}$$