Can the nos. 14x + 5/9 and 17x - 4/12 both be the integers for some integer x? If so find the integers.

We need to find whether the nos. 14x + 5/9 and 17x - 4/12 both be the integers for some integer x.

So,

This type of questions can be solved by hit and trial method.

We should start checking with values of x starting from 1,2,3,.......

By observation we can see that for x=8 both m(=11) and n(=13) are integers.