Solve 4/8-5/9x+2/3+3/7x=frac{217}{5}

$$\frac { 4 } { 8 } - \frac { 5 } { 9 } x + \frac { 2 } { 3 } + \frac { 3 } { 7 } x = \frac { 217 } { 5 }$$

Solve for x

$$x = -\frac{26607}{80} = -332\frac{47}{80} = -332.5875$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}-\frac{5}{9}x+\frac{2}{3}+\frac{3}{7}x=\frac{217}{5}$$

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

$$\frac{3}{6}-\frac{5}{9}x+\frac{4}{6}+\frac{3}{7}x=\frac{217}{5}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{6}-\frac{5}{9}x+\frac{3}{7}x=\frac{217}{5}$$

Add 3 and 4 to get 7.

$$\frac{7}{6}-\frac{5}{9}x+\frac{3}{7}x=\frac{217}{5}$$

Combine -\frac{5}{9}x and \frac{3}{7}x to get -\frac{8}{63}x.

$$\frac{7}{6}-\frac{8}{63}x=\frac{217}{5}$$

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

$$-\frac{8}{63}x=\frac{217}{5}-\frac{7}{6}$$

Least common multiple of 5 and 6 is 30. Convert \frac{217}{5} and \frac{7}{6} to fractions with denominator 30.

$$-\frac{8}{63}x=\frac{1302}{30}-\frac{35}{30}$$

Since \frac{1302}{30} and \frac{35}{30} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{8}{63}x=\frac{1302-35}{30}$$

Subtract 35 from 1302 to get 1267.

$$-\frac{8}{63}x=\frac{1267}{30}$$

Multiply both sides by -\frac{63}{8}, the reciprocal of -\frac{8}{63}.

$$x=\frac{1267}{30}\left(-\frac{63}{8}\right)$$

Multiply \frac{1267}{30} times -\frac{63}{8} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1267\left(-63\right)}{30\times 8}$$

Do the multiplications in the fraction \frac{1267\left(-63\right)}{30\times 8}.

$$x=\frac{-79821}{240}$$

Reduce the fraction \frac{-79821}{240} to lowest terms by extracting and canceling out 3.

$$x=-\frac{26607}{80}$$