To add x/2 and x/5 together, we note that the least common denominator between 2 and 5 is 10. Using this fact, we can turn x/2 into the equivalent fraction 5x/10, and x/5 into 2x/10. Adding the two together gets us
5x/10 + 2x/10 = 7x/10
Now, our equation reads
7x/10 = 5/4
Cross multiplying, this equation implies that
7x(4) = 10(5), or
28x = 50.
Dividing either side by 28, we find that
x = 50/28 = 25/14
To verify this, we can substitute this value in for x in the original equation to get
(25/14)/2 + (25/14)/5
For the first term, half of 1/14 is 1/28, so half of 25/14 should give us 25/28. For the second, 1/5 of 25 is 5, so 1/5 of 25/14 is appropriately 5/14, or 10/28.
25/28 + 10/28 = 35/28, and since 35 and 28 have a common factor of 7 (35 = 7 x 5, 28 = 7 x 4), we can reduce 35/28 to 5/4, showing that our answer checks out.
