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

1 Answer
May 27, 2016

Answer:

#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