Question

Solve algebriacally.

Answer 1

solve what?

Answer 2

\[x^3-4x^2-12x < 0\]

Answer 3

then do it?

Answer 4

x(x^2-4x-12) <0

Answer 5

x(x-6)(x+4) <0

Answer 6

that right?

Answer 7

x(x^2 -4x-12)<0
x(x^2 -6x+2x-12)<0
x{x(x-6)+2(x-6)}<0
x(x-6)(x-2)<0
i think after this you can do

Answer 8

foil out (x-6)(x-2)= x^2-8x+12

Answer 9

sorry sorry last one would be
x(x^2 -4x-12)<0
x(x^2 -6x+2x-12)<0
x{x(x-6)+2(x-6)}<0
x(x-6)(x+2)<0 sorry yes it would be (x+2) instead of (x-2)

Answer 10

i meant to type this earlier
x(x-6)(x+2) < 0

Answer 11

so whats next? ik u set each thing equal to 0 but then is it just x<0, x<6, x<-2 ???

Answer 12

do you have to find a interval

Answer 13

no its just says solve algebraically

Answer 14

-2<x<6

Answer 15

im GUESSING i need an interval tho...

Answer 16

just gave it to u

Answer 17

so its x>-2 instead of x<-2 cuz if u go across the < sign you have to switch it right???

Answer 18

???

Answer 19

for x: 0 < x < 6, then the first parenthesis term (x) is positive, the second term is negative, and the third is positive, so the overall inequality holds.

for x: x< -2, then the first term is negative, the second is negative, and the third is negative, so overall the expression < 0 and the inequality holds.

so there are two regions where the inequality is true... 0<x<6 and x<-2

Answer 20

no making interval is different do one thing put any value less that -2 put - 3 what do you get os the expression is still less than zero no put any value greater than 6 say the expression would still not be less than zero now put value of c=4, 5 , 1 ,2 it would be less than zero u have to find an interval in which the the value of expression in less than zero and that is -2<x<6

Answer 21

but why is it x<6 and x>-2 in stead of x<-2

Answer 22

is it because you go across the < sign when you solve???

Answer 23

sorry sorry i made a mistake x<0 and x <-2 so this means that x<0 this you so x can assume any value between
\[- \infty <x <0\]
but is x<6
so interval would be \[- \infty<x<6\]

Answer 24

x = -1 doesn't work

Answer 25

the interval runs from 0 < x < 6 and then resumes for x < -2

Answer 26

@JakeV8 u r right it slipped my mind it would be a union interval