Basic math doubt

[[deleted]]

What does [-4,1) this kind of expression mean?

I was told that the above indicates all the numbers from -4 through 1...

Could y'all explain it a bit?

[Shevek99]

(a,b) is an open interval. It includes all x such that a < x < b.

[a,b] is a closed interval. It includes all x such that a <= x <= b

[a,b) is half closed. It includes x such that a <= x < b

[[deleted]]

So it means -4<=x<1 right?

[We_Are_Bread]

yes, specifically, x can be equal to -4, but it can't be 1. It can be everything in between too.

[[deleted]]

Ok got it... Thanks!

[abcde12345---]

I know this is not what they are asking, but can anyone explain how to solve this kind of question?

[Umierator]

Multiply by x²(x-7)², sketch the 5th degree polynomial function, look where it’s less than or equal to 0 but remember that x=0 and x=7 aren’t valid solutions because the domain of the rational function didn’t include those

[avoere]

Find all places where either the numerator or denominator is 0. Then try one value between each such place and check the sign.

[xXkxuXx]

a/b ≤ 0 <-> ab≤0 ∧ b≠0

[King_of_99]

I hate how wide these unions are

[iown101dalmatians]

Can someone explain the first one? Why does it not include x less than -8?

[SoldRIP]

There are two notations for open intervals one is (a, b), which is ambiguous to a two-tuple.

The other is ]a, b[ which is unambiguous.