Solve 10/10x+2/7<10/8+10/8

$$\frac { 10 } { 10 } x + \frac { 2 } { 7 } < \frac { 10 } { 8 } + \frac { 10 } { 8 }$$

Solve for x

$$x<\frac{31}{14}$$

Solution Steps

Divide 10 by 10 to get 1.

$$1x+\frac{2}{7}<\frac{10}{8}+\frac{10}{8}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$1x+\frac{2}{7}<\frac{5}{4}+\frac{10}{8}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$1x+\frac{2}{7}<\frac{5}{4}+\frac{5}{4}$$

Since \frac{5}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$1x+\frac{2}{7}<\frac{5+5}{4}$$

Add 5 and 5 to get 10.

$$1x+\frac{2}{7}<\frac{10}{4}$$

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

$$1x+\frac{2}{7}<\frac{5}{2}$$

Subtract \frac{2}{7} from both sides.

$$1x<\frac{5}{2}-\frac{2}{7}$$

Least common multiple of 2 and 7 is 14. Convert \frac{5}{2} and \frac{2}{7} to fractions with denominator 14.

$$1x<\frac{35}{14}-\frac{4}{14}$$

Since \frac{35}{14} and \frac{4}{14} have the same denominator, subtract them by subtracting their numerators.

$$1x<\frac{35-4}{14}$$

Subtract 4 from 35 to get 31.

$$1x<\frac{31}{14}$$

Divide both sides by 1. Since 1 is positive, the inequality direction remains the same.

$$x<\frac{\frac{31}{14}}{1}$$

Express \frac{\frac{31}{14}}{1} as a single fraction.

$$x<\frac{31}{14\times 1}$$

Multiply 14 and 1 to get 14.

$$x<\frac{31}{14}$$