Solve 1/5-1/7-x+1/63=1/15

$$\frac{ 1 }{ 5 } - \frac{ 1 }{ 7 } -x+ \frac{ 1 }{ 63 } = \frac{ 1 }{ 15 }$$

Solve for x

$$x=\frac{2}{315}\approx 0.006349206$$

Steps for Solving Linear Equation

Least common multiple of 5 and 7 is 35. Convert \frac{1}{5} and \frac{1}{7} to fractions with denominator 35.

$$\frac{7}{35}-\frac{5}{35}-x+\frac{1}{63}=\frac{1}{15}$$

Since \frac{7}{35} and \frac{5}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-5}{35}-x+\frac{1}{63}=\frac{1}{15}$$

Subtract 5 from 7 to get 2.

$$\frac{2}{35}-x+\frac{1}{63}=\frac{1}{15}$$

Least common multiple of 35 and 63 is 315. Convert \frac{2}{35} and \frac{1}{63} to fractions with denominator 315.

$$\frac{18}{315}-x+\frac{5}{315}=\frac{1}{15}$$

Since \frac{18}{315} and \frac{5}{315} have the same denominator, add them by adding their numerators.

$$\frac{18+5}{315}-x=\frac{1}{15}$$

Add 18 and 5 to get 23.

$$\frac{23}{315}-x=\frac{1}{15}$$

Subtract \frac{23}{315} from both sides.

$$-x=\frac{1}{15}-\frac{23}{315}$$

Least common multiple of 15 and 315 is 315. Convert \frac{1}{15} and \frac{23}{315} to fractions with denominator 315.

$$-x=\frac{21}{315}-\frac{23}{315}$$

Since \frac{21}{315} and \frac{23}{315} have the same denominator, subtract them by subtracting their numerators.

$$-x=\frac{21-23}{315}$$

Subtract 23 from 21 to get -2.

$$-x=-\frac{2}{315}$$

Multiply both sides by -1.

$$x=\frac{2}{315}$$