Solving Inequalities: h(t) > 25

[zeion]

Homework Statement

I have a function h(t) = 30t - 5t^2.
I need to find the interval for which h is > 25.

Homework Equations

The Attempt at a Solution

h(t) = 30t - 5t² - 25 > 0
-5(t² - 6t + 5) > 0
iff t² - 6t + 5 > 0
Then the answer is t > 5 and t < 1.

But it is actually between those points.
Is it because I factored out a negative?

 

[zgozvrm]

In your last step, you get rid of the -5 by multiplying each side by -1/5.
This effectively reverses the inequality sign.

You may want to think of it another way...
You could add 5(t² - 6t + 5) to both sides, which would give you
0 > 5(t² - 6t + 5)

 

[zeion]

oicic ty

 

[zgozvrm]

Not being a "texter," I'll assume that means "Oh, I see, I see. Thank you"

You're welcome!
(or, should I say, "yw"?)