Solve (1/5(x-10)>1/10-2/15

$$( \frac { 1 } { 5 } ( x - 10 ) > \frac { 1 } { 10 } - \frac { 2 } { 15 }$$

Solve for x

$$x>\frac{59}{6}$$

Solution Steps

Use the distributive property to multiply \frac{1}{5} by x-10.

$$\frac{1}{5}x+\frac{1}{5}\left(-10\right)>\frac{1}{10}-\frac{2}{15}$$

Multiply \frac{1}{5} and -10 to get \frac{-10}{5}.

$$\frac{1}{5}x+\frac{-10}{5}>\frac{1}{10}-\frac{2}{15}$$

Divide -10 by 5 to get -2.

$$\frac{1}{5}x-2>\frac{1}{10}-\frac{2}{15}$$

Least common multiple of 10 and 15 is 30. Convert \frac{1}{10} and \frac{2}{15} to fractions with denominator 30.

$$\frac{1}{5}x-2>\frac{3}{30}-\frac{4}{30}$$

Since \frac{3}{30} and \frac{4}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}x-2>\frac{3-4}{30}$$

Subtract 4 from 3 to get -1.

$$\frac{1}{5}x-2>-\frac{1}{30}$$

Add 2 to both sides.

$$\frac{1}{5}x>-\frac{1}{30}+2$$

Convert 2 to fraction \frac{60}{30}.

$$\frac{1}{5}x>-\frac{1}{30}+\frac{60}{30}$$

Since -\frac{1}{30} and \frac{60}{30} have the same denominator, add them by adding their numerators.

$$\frac{1}{5}x>\frac{-1+60}{30}$$

Add -1 and 60 to get 59.

$$\frac{1}{5}x>\frac{59}{30}$$

Multiply both sides by 5, the reciprocal of \frac{1}{5}. Since \frac{1}{5} is positive, the inequality direction remains the same.

$$x>\frac{59}{30}\times 5$$

Express \frac{59}{30}\times 5 as a single fraction.

$$x>\frac{59\times 5}{30}$$

Multiply 59 and 5 to get 295.

$$x>\frac{295}{30}$$

Reduce the fraction \frac{295}{30} to lowest terms by extracting and canceling out 5.

$$x>\frac{59}{6}$$