Solve 2/5x(-3/7)-1/6+3/2+frac{1}{14}-xfrac{2}{5}

$$\frac { 2 } { 5 } x ( - \frac { 3 } { 7 } ) - \frac { 1 } { 6 } + \frac { 3 } { 2 } + \frac { 1 } { 14 } - x \frac { 2 } { 5 }$$

Evaluate

$$-\frac{4x}{7}+\frac{59}{42}$$

Solution Steps

Multiply \frac{2}{5} times -\frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-3\right)}{5\times 7}x-\frac{1}{6}+\frac{3}{2}+\frac{1}{14}-x\times \frac{2}{5}$$

Do the multiplications in the fraction \frac{2\left(-3\right)}{5\times 7}.

$$\frac{-6}{35}x-\frac{1}{6}+\frac{3}{2}+\frac{1}{14}-x\times \frac{2}{5}$$

Fraction \frac{-6}{35} can be rewritten as -\frac{6}{35} by extracting the negative sign.

$$-\frac{6}{35}x-\frac{1}{6}+\frac{3}{2}+\frac{1}{14}-x\times \frac{2}{5}$$

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

$$-\frac{6}{35}x-\frac{1}{6}+\frac{9}{6}+\frac{1}{14}-x\times \frac{2}{5}$$

Since -\frac{1}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$-\frac{6}{35}x+\frac{-1+9}{6}+\frac{1}{14}-x\times \frac{2}{5}$$

Add -1 and 9 to get 8.

$$-\frac{6}{35}x+\frac{8}{6}+\frac{1}{14}-x\times \frac{2}{5}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{6}{35}x+\frac{4}{3}+\frac{1}{14}-x\times \frac{2}{5}$$

Least common multiple of 3 and 14 is 42. Convert \frac{4}{3} and \frac{1}{14} to fractions with denominator 42.

$$-\frac{6}{35}x+\frac{56}{42}+\frac{3}{42}-x\times \frac{2}{5}$$

Since \frac{56}{42} and \frac{3}{42} have the same denominator, add them by adding their numerators.

$$-\frac{6}{35}x+\frac{56+3}{42}-x\times \frac{2}{5}$$

Add 56 and 3 to get 59.

$$-\frac{6}{35}x+\frac{59}{42}-x\times \frac{2}{5}$$

Combine -\frac{6}{35}x and -x\times \frac{2}{5} to get -\frac{4}{7}x.

$$-\frac{4}{7}x+\frac{59}{42}$$

Factor

$$\frac{59-24x}{42}$$

Solution Steps

Factor out \frac{1}{210}.

$$\frac{-120x+295}{210}$$

Consider -36x-35+315+15-84x. Multiply and combine like terms.

$$-120x+295$$

Consider -120x+295. Factor out 5.

$$5\left(-24x+59\right)$$

Rewrite the complete factored expression.

$$\frac{-24x+59}{42}$$