x² < 7x
x² - 7x < 0
x(x - 7) < 0
the zeros of the left side are 0 and 7,
the critical numbers.
We test a point in the three intervals:
(-∞,0), (0, 7), (7,∞)
-1(-1 - 7) < 0
8 < 0 false, so not (-∞,0),
1(1 - 7) < 0
-7 < 0 true, so (0,7)
8(8 - 7) < 0
8 < 0 false, so not (7,∞)
Therefore the only integers that satisfy
the given inequality are the integers in (0,7),
which are {1,2,3,4,5,6}.
Edwin
