Solve 5/6x-2/5>3/4x-1/10

$$\frac { 5 } { 6 } x - \frac { 2 } { 5 } > \frac { 3 } { 4 } x - \frac { 1 } { 10 }$$

Solve for x

$$x>\frac{18}{5}$$

Solution Steps

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

$$\frac{5}{6}x-\frac{2}{5}-\frac{3}{4}x>-\frac{1}{10}$$

Combine \frac{5}{6}x and -\frac{3}{4}x to get \frac{1}{12}x.

$$\frac{1}{12}x-\frac{2}{5}>-\frac{1}{10}$$

Add \frac{2}{5} to both sides.

$$\frac{1}{12}x>-\frac{1}{10}+\frac{2}{5}$$

Least common multiple of 10 and 5 is 10. Convert -\frac{1}{10} and \frac{2}{5} to fractions with denominator 10.

$$\frac{1}{12}x>-\frac{1}{10}+\frac{4}{10}$$

Since -\frac{1}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.

$$\frac{1}{12}x>\frac{-1+4}{10}$$

Add -1 and 4 to get 3.

$$\frac{1}{12}x>\frac{3}{10}$$

Multiply both sides by 12, the reciprocal of \frac{1}{12}. Since \frac{1}{12} is positive, the inequality direction remains the same.

$$x>\frac{3}{10}\times 12$$

Express \frac{3}{10}\times 12 as a single fraction.

$$x>\frac{3\times 12}{10}$$

Multiply 3 and 12 to get 36.

$$x>\frac{36}{10}$$

Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$x>\frac{18}{5}$$