# Doubt in an inequality problem

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1. Dec 1, 2016

### Thiru07

1. The problem statement, all variables and given/known data
Given : (y+2)(y-3) <= 0

2. Relevant equations

3. The attempt at a solution
Now, I have y-3 <= 0 or y+2 <= 0
Hence, y <= 3 or y <= -2
But how
is correct?
I think
is wrong because y <= -2.

2. Dec 1, 2016

### PeroK

You could draw a graph of $(y+2)(y-3)$ to see what's happening.

What happens if both $y+2 < 0$ and $y-3 < 0$?

3. Dec 1, 2016

### Thiru07

In that case , we will keep y < -2 and ignore y < 3.
I think I got it. We have to ignore y+2 <= 0 and y-3 >=0 as
is not possible and keep
Thanks PeroK :)

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4. Dec 1, 2016

### Staff: Mentor

No, the above doesn't follow from the inequality. I think you might already have solved this inequality, but showing where you went wrong is worthwhile.
For the product of two expressions to be negative, one of them has to be negative, and the other has to be positive. Since this can happen in either of two ways, you need to examine two different cases.