Question

The values of x that satisfy the inequality 2x-3/(x+4) <-3 lie in the interval?

Answer 1

afraid i do not see any inequality here

Answer 2

sorry

Answer 3

plzz view the question now

Answer 4

is it
\[\frac{2x-3}{x+4}<0\] or maybe
\[2x-3<x+4\]?

Answer 5

\[\frac{2x-3}{x+4}<-3\] like this?

Answer 6

yes

Answer 7

first add 3 to both sides to get
\[\frac{2x-3}{x+4}+3<0\]
then add to get
\[\frac{2x-3}{x+4}+3=\frac{2x-3+3(x+4)}{x+4}\]
\[=\frac{2x-3+3x+12}{x+4}=\frac{5x-9}{x+4}\]

Answer 8

ok then...

Answer 9

now your inequality looks like
\[\frac{5x-9}{x+4}<0\] and you should be good to go

Answer 10

hey but the answer should be (-4 , -9/5)

Answer 11

find the zeros of each factor. they are -4 and 9/5

Answer 12

how???

Answer 13

oh right, because i made a mistake it is 12 -3 =9 not -9 so it should be
\[\frac{5x+9}{x+4}<0\] not what i wrote

Answer 14

ok i want to know how that -4 came........

Answer 15

that's better.
\(x+4=0\) if \(x=-4\) and \(2x+9=0\) if \(x=-\frac{9}{5}\)

Answer 16

so the quotient \(\frac{5x+9}{x+4}\) will be negative (less than zero) between these numbers, in other words in the interval \((-4,-\frac{9}{5})\)

Answer 17

so you see where the "-4" came from? it is the value of \(x\) that will make the denominator equal to zero

Answer 18

if we take x+4 to that side it will be 0

Answer 19

i am not sure what you mean. if you write
\[x+4=0\] you get
\[x=-4\]

Answer 20

and if you set
\[5x+9=0\] you get
\[x=-\frac{9}{5}\] which i hope explains where the endpoints of the interval come from

Answer 21

ok i got it......

Answer 22

you also need to remember that you are asking where this quotient is negative, and it will be negative between the zeros and positive outside them

Answer 23

ok plzz help @satellite73 new question on maths page http://openstudy.com/study?signup#/updates/4fbf7453e4b0dd370c77304f