Question

Please somebody- It's just a simple check to see if I have the right answer (pretty easy) :)

Just want to check if this is correct in interval notation.
Solve the inequality, write in interval or union of interval notation:
x^3+x^2<=9x+9

Answer: (x <= -3] and [-1<=x<=3]

Interval notation: (-infinity, -3] U [-1,3]

Answer 1

correct

Answer 2

Really?

Answer 3

Are you sure it's a union @mathgeek!

Answer 4

@amistre64 Can you double check this for me please?

Answer 5

ya one sec

Answer 6

1st equation:
x^3+x^2-9x-9
Break it up in two parts

x^3+x^2 and -9x-9

Pull out common factors

x^2(x+1) and -9(x+1)

Since (x+1) match on both sides just use it once, then put the outside terms in another group

(x+1)(x^2-9)

Then see if the terms cant be reduced further

(x+1)(x+3)(x-3)

2nd equation

Basically there isn't an easy way to do this. Just try to remember what cubic factoring looks like. It is all similar to this.

(y+1)(y^2-y+1)

Answer 7

thats what i got

Answer 8

essential i get a boundary line:

x^3+x^2 = 9x+9

x^3+x^2 - 9x- 9 = 0

which breaks into 3 parts: (x+3)(x+1)(x-3); zeros are x=3,-1,-3

mark these as 0s on a number line



<----------0--------0--------0----------->
-3 -1 3

now we can determine the sign value for the 4 segments that are NOT 0, simply pick a value and test it out

-5 -2 0 5
<----------0--------0--------0----------->
-3 -1 3
-64 5 -9 96

so we have a map that is: -, + -, + and we want all the segments that are 0 or positive

x = [-3,-1] OR [3,inf)

Answer 9

pffft, that was spose to be a <= 0

Answer 10

x = (-inf,-3] OR [-1,3]

Answer 11

i was right though

Answer 12

Lol-You lost me on the boundary line amistre. So I can put either (-inf, -3] as the correct answer OR [-1,-3]?

Answer 13

if its asking for ALL values that make it a solution; you have to use the OR and include both ranges

Answer 14

exactly

Answer 15

mathgeek! was correct ;)

the boundary line was a thought i had if we were going to graph this on paper .... it was a spurious thought

Answer 16

hahah u can call me emilee my username is pretty stupid

Answer 17

gotcha- it doesn't ask for the range it just asks me to solve the inequality in interval or union of interval notation. When I got the second [-1,3] i threw me off...

Answer 18

thank you emilee :)