If (x + 3) (x - 2) > 0
then solving by regular/shorter method would give us
x + 3 > 0 , x - 2 > 0
x > - 3 , x > 2
But via the longer method, we see that x < - 3.
I wanted to check if I’m solving this incorrectly. Any help would be appreciated. Thank you.
Which has a flaw. You’re working on the basis that the product of two positive numbers is positive. This is true. But what about when both numbers are negative?
Thank you, I got your point. So then if we were to solve this inequality just via the shorter method, how would we arrive at a definite answer?
Apply the process twice (once when both are positive, and once when both are negative) and combine the result.
I understand your point logically. I was wondering if you could illustrate the same for me?
Thank you.
Part 1: (x + 3) > 0 and (x - 2) > 0 → x > -3 and x > 2. If x > 2, x > -3, so this combines to x > 2.
Part 2: (x + 3) < 0 and (x - 2) < 0 → x < -3 and x < 2. If x < -3, x < 2, so this combines to x < -3.
Combining the two parts together, we get x < -3 and x > 2.
Thank you so much.
