Question

Can someone PLEASE help me out with Inequality? SOS

Answer 1

\[X>7 or -2<X<6 or X \le-3\]

Answer 2

that's the answer, and I don't understand how to do that!

Answer 3

PLEASE @Emeyluv99 ?

Answer 4

factorize the top and the bottom separately first

Answer 5

you mean =0?

Answer 6

yes

Answer 7

so we get (x+3)((x-6) for the nominator

Answer 8

and for the denominator we get (x-7)(x+2)

Answer 9

ok, now, what values of x cannot work

Answer 10

\[\frac{ (x-6)(x+3) }{ (x-7)(x+2) }\]

Answer 11

7 and 2

Answer 12

right?

Answer 13

but how from here?

Answer 14

can you please show how to calculate from here?

Answer 15

@Emeyluv99

Answer 16

sorru. computers being mean.. and be careful, its 7 and -2

Answer 17

now the way I would do it, graph the quadratic you get in the numerator. See what values of x give a positive y and that's you're answer. Be careful to exclude 7 and -2 though

Answer 18

that's what I did but I didn't get the asnswer

Answer 19

from graphing you should get x<-3 and x>6... but, since we can't have 7 you should get X<-3, 6<x<7, and x>7

Answer 20

but that's not the answer... thanks though

Answer 21

@ganeshie8 will you be savior?

Answer 22

my

Answer 23

pick any number to the left of -3
say -4

plug x = -4 in the given inequality

Answer 24

\[\frac{ (x-6)(x+3) }{ (x-7)(x+2)}\]
plugging x=-4 gives
\[\frac{ (-4-6)(-4+3) }{ (-4-7)(-4+2) }\]

looks it is positive, yes ?

Answer 25

yes

Answer 26

but why would you put -4 from the first place?

Answer 27

?

Answer 28

you can put any number to the left of -3 for testing
since -4 is easy to work..

Answer 29

oh ok, then what am I doing from here?

Answer 30

since a number to the left of -3 satisfies the inequality, \(x\lt 3\) is part of the solution :