Question

How do you solve inequalities with products?
\[x(x-1)(x+2) > 0\]

Answer 1

You need first to find where the LHS of the inequality is equal to zero

Answer 2

what do you mean?

Answer 3

\[x=0, x=1, x=-2\]

Answer 4

All the above value will make the LHS of the inequality 0 .. right?

Answer 5

what do you mean inequality 0?

Answer 6

The LHS of the inequality

Answer 7

x(x-1)(x+2)=0 when

x=0, x=1, and x=-2

Answer 8

i get that

Answer 9

So, then you ask yourself: what are the options that make LHS positive?

+ + +
- - +
- + -
+ - -

Answer 10

following so far

Answer 11

ahh yes i see it

Answer 12

+ + + means x>0 and x>1, and x>-2 (take the intersection of those 3 intervals) you get x>1

Answer 13

so the solution is just x > 1?

Answer 14

that is only for the first possibility + + +

Answer 15

so there are more huh

Answer 16

You need to check for the rest..and be careful..some of the other possibility may not have a solution

Answer 17

isn't the solution x < 0, x > 1 and x < -2?

Answer 18

Do you want me to cont, explaining

Answer 19

since if x < 0 it would be negative
x < - 2 => negative
x > 1 => positive

Answer 20

take for example...

- - + which means

x<0, x<1, and x>-2

-2<x<1

Answer 21

- - +

x<0, x<1, and x>-2 .. means that -2<x<0

Answer 22

so we have so far

x>1 or -2<x<0

Answer 23

check for - + - ...and so on