(x - 1)(x2 - 9x + 18) <= 0
Don't expand; separate the parts:
For (X)(Y) <= 0, there are two possibilites:
Either X is positive and Y is negative
or X is negative and Y is positive.
So:
Either (x - 1 ) >= 0 and (x2 - 9x + 18) <= 0
or (x - 1 ) <= 0 and (x2 - 9x + 18) >= 0.
Case 1: (x - 1 ) >= 0 and (x2 - 9x + 18) <= 0
x - 1 > = 0 and (x - 6)(x - 3) <= 0
x >= 1 and 3 <= x <= 6
3 <= x <= 6
Case 2: (x - 1 ) <= 0 and (x2 - 9x + 18) >= 0
x - 1 <= 0 and (x - 6)(x - 3) >= 0
x <= 1 and [ x <= 3 or x >= 6 ]
x <= 1