Solve (x-2)(x+1)(x+3) < 0?

Question

can someone help me with this please? thanks

Answer 1

Because you have three terms multiplied, either only 1 can be negative or all 3 have to be (in order for the final answer to be <0). Remember a negative times a negative = positive, but a negative times a negative times a negative = negative!
So you have a few answers,
x< 2 will give you one negative term
or x<-3 will give you all negative terms
But you can't have between -3 and -1
So your answer will be x<-3 and x>-1 and x<2

Answer 2

You have the product of 3 numbers. It will be negative if, and only if, one is negative and the other 2 are positive, or if 2 are negative and the other is positive or if the 3 numbers are negative.

If x < -3, then all the 3 expressions give negative numbers, so that their product is negative.

-If -3 < x < -1, then x + 3 >0, x -1 < 0 and x -2 < 0, so that the product is positive.

If -1 < x < 2, a similar reasoning shows the product is negative

And if x > 2 then the product is positive.

So, (x-2)(x+1)(x+3) < 0 if, and only if x is in (-oo, -3) Union (-1, 2)

Answer 3

Ever heard of P E M D A S?

Do the ( ) first.
(x-2)(x+1)(x+3) < 0
(x²-x-2)(x+3)<0

do the rest.

Answer 4

you have three things being multiplied together:

(x-2)(x+1)(x+3) and that must be negative (<0)

so if you're multiplting three things together and they have to be negative then your scenarios are as follows:

1) (x-2) is negative and (x+1) and (x+3) are positive (-++)
this'll give you x = (-1,2)
2) (x-2) and (x+1) are positive and (x+3) is negative (++-)
this one can't happen
3) (x-2) and (x+3) are positive and (x+1) is negative (+-+)
this one can't happen
4) they're all negative (---)
this gives you x<-3

your answer is x=(-1,2) (x is in between -1 and 2, not including -1 or 2)

OR

x<-3

Answer 5

(x-2)(x+1)(x+3)<0

(x+1)(x+3)<0

x+2<0
-2 -2
-----------
x<-2

x<2

Answer 6

that is no longer a sprint, that is a intense component to the priority. in simple terms take the | | value as being effective, then unfavourable. There are 4 combos obtainable. Then sparkling up each and all the 4 equations.

Answer 7

x can be from negative infinity to -3 (not inclusive), or x can be between -1 and +2 (not inclusive).

Answer 8

=x(cube)-3x-2