To solve the inequality x - 2 < 0, we can add 2 to both sides of the inequality:

x - 2 + 2 < 0 + 2
x < 2

So the solution to the inequality x - 2 < 0 is x < 2.

To solve the inequality x^2(x - 2) > 0, we can first find the critical points by setting each factor equal to zero:

x^2 = 0
x = 0

x - 2 = 0
x = 2

Now we can create a number line and test the intervals between the critical points:

Test x < 0:
(-1)^2(-1 - 2) > 0
1(-3) > 0
-3 > 0
This is false.

Test 0 < x < 2:
(1)^2(1 - 2) > 0
1(-1) > 0
-1 > 0
This is false.

Test x > 2:
(3)^2(3 - 2) > 0
9(1) > 0
9 > 0
This is true.

Therefore, the solution to the inequality x^2(x - 2) > 0 is x > 2.

In summary, the solutions to the given inequalities are x < 2 and x > 2.