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

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

Solve for x

$$x = -\frac{31}{18} = -1\frac{13}{18} \approx -1.722222222$$

Steps for Solving Linear Equation

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{3}{7}=\frac{9}{6}-\frac{2}{6}+\frac{3}{7}x$$

Since \frac{9}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{7}=\frac{9-2}{6}+\frac{3}{7}x$$

Subtract 2 from 9 to get 7.

$$\frac{3}{7}=\frac{7}{6}+\frac{3}{7}x$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{7}{6}+\frac{3}{7}x=\frac{3}{7}$$

Subtract \frac{7}{6} from both sides.

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

Least common multiple of 7 and 6 is 42. Convert \frac{3}{7} and \frac{7}{6} to fractions with denominator 42.

$$\frac{3}{7}x=\frac{18}{42}-\frac{49}{42}$$

Since \frac{18}{42} and \frac{49}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{7}x=\frac{18-49}{42}$$

Subtract 49 from 18 to get -31.

$$\frac{3}{7}x=-\frac{31}{42}$$

Multiply both sides by \frac{7}{3}, the reciprocal of \frac{3}{7}.

$$x=-\frac{31}{42}\times \frac{7}{3}$$

Multiply -\frac{31}{42} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-31\times 7}{42\times 3}$$

Do the multiplications in the fraction \frac{-31\times 7}{42\times 3}.

$$x=\frac{-217}{126}$$

Reduce the fraction \frac{-217}{126} to lowest terms by extracting and canceling out 7.

$$x=-\frac{31}{18}$$