Solve 2/5x+3/4<6/2x+4/10

$$\frac { 2 } { 5 } x + \frac { 3 } { 4 } < \frac { 6 } { 2 } x + \frac { 4 } { 10 }$$

Solve for x

$$x>\frac{7}{52}$$

Solution Steps

Divide 6 by 2 to get 3.

$$\frac{2}{5}x+\frac{3}{4}<3x+\frac{4}{10}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}x+\frac{3}{4}<3x+\frac{2}{5}$$

Subtract 3x from both sides.

$$\frac{2}{5}x+\frac{3}{4}-3x<\frac{2}{5}$$

Combine \frac{2}{5}x and -3x to get -\frac{13}{5}x.

$$-\frac{13}{5}x+\frac{3}{4}<\frac{2}{5}$$

Subtract \frac{3}{4} from both sides.

$$-\frac{13}{5}x<\frac{2}{5}-\frac{3}{4}$$

Least common multiple of 5 and 4 is 20. Convert \frac{2}{5} and \frac{3}{4} to fractions with denominator 20.

$$-\frac{13}{5}x<\frac{8}{20}-\frac{15}{20}$$

Since \frac{8}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{5}x<\frac{8-15}{20}$$

Subtract 15 from 8 to get -7.

$$-\frac{13}{5}x<-\frac{7}{20}$$

Multiply both sides by -\frac{5}{13}, the reciprocal of -\frac{13}{5}. Since -\frac{13}{5} is negative, the inequality direction is changed.

$$x>-\frac{7}{20}\left(-\frac{5}{13}\right)$$

Multiply -\frac{7}{20} times -\frac{5}{13} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{-7\left(-5\right)}{20\times 13}$$

Do the multiplications in the fraction \frac{-7\left(-5\right)}{20\times 13}.

$$x>\frac{35}{260}$$

Reduce the fraction \frac{35}{260} to lowest terms by extracting and canceling out 5.

$$x>\frac{7}{52}$$