algebra HELP!?

Question

How do I solve the polynomial inequality?!

(x + 3)(x - 6) < 0

Answer 1

This will be negative when (x+3) is negative and (x-6) is positive, or vice versa.

First case:
x+3 < 0 --> x < -3
x-6 > 0 --> x > 6

This has no solution because x can't be smaller than -3 and bigger than 6.

Second case:
x+3 > 0 --> x > -3
x-6 < 0 --> x < 6

This is true when x is greater than -3 and less than 6.

So the answer is when x is between -3 and 6
-3 < x < 6