Question 1182468
<br>
Of course the problem is quickly and easily solved without formal mathematics:
1 and 2
2 and 3
3 and 4
4 and 5<br>
But if this is an exercise in setting up problems for solving using formal mathematics....<br>
x = smaller integer
x+1 = larger integer<br>
The sum of the two integers is less than 10:
(x)+(x+1) < 10
2x+1 < 10
2x < 9
x < 4.5<br>
The smaller integer is positive and less than 4.5; the possibilities are 1, 2, 3, and 4 -- leading, of course, to the set of pairs above.<br>