Question

How do you solve `1/5+1/x=1/2`?

Answer 1

`x=10/3`

Explanation:

First, we eliminate the fractions from the equation by multiplying by the least common multiple of all denominators. As none of the denominators share any prime factors, the least common multiple is `5xx x xx 2 = 10x`

`1/5+1/x = 1/2`

`=> 10x(1/5+1/x)=10x(1/2)`

`=> (10x)/5+(10x)/x=(10x)/2`

`=> 2x+10 = 5x`

`=> 5x - 2x = 2x + 10 - 2x`

`=> 3x = 10`

`=> (3x)/3 = 10/3`

`:. x = 10/3`

Finally, we check our answer by plugging in our result:

`1/5+1/(10/3) = 1/5+3/10`

`=2/10+3/10`

`=5/10`

`=1/2` as desired