Question

find x
(x-5)/(3-x)<0
and no the answer isn't x<5

Answer 1

u say x<5 lets take 4
then we will have (-1)/(-1) and this is equal to +1 after that we can see it is not correct because 1>0

Answer 2

yes i know that, thats why I said x<5 isn't an answer

Answer 3

if the answer is x<5 i think the answer is wrong

Answer 4

but it IS NOT (and i mean NOT) the answer gesh read it right

Answer 5

i couldnt understand you sorry

Answer 6

it's x>5

Answer 7

how did you get that? ( i need to show work + understand)

Answer 8

times both sides by (3-x) and since you are multiplying by a negative x, the inequality changes the sign. the rest is easy.

Answer 9

did you get this?

Answer 10

\[\frac{x-5}{3-x}<0\]

Answer 11

answer is

\[(-\infty,3)\cup(5,\infty)\]

Answer 12

how did you get that?

Answer 13

consider the two factors separately.

\[x-5<0\] if
\[x<5\] and
\[3-x<0\] if
\[x>3\] now compare.
if
\[x<3\]
then
\[x-3>0\] and 0\[x-5<0\] and a positive times a negative is negative

Answer 14

my guess is this is not clear so lets make a chart

Answer 15

x - 5 ------------------------ 5 +++++++++++
3-x ++++++++++3 ---------------------------

together --------------3+++++++5----------------

Answer 16

yeah u guess right

Answer 17

so if x < 3 it is negative, and if x > 5 it is negative, and between 3 and 5 it is positive

Answer 18

you can also do the following.
pick a number less than 3 and test by replacing in the expression. it will be negative
pick a number betwen 3 and 5 and test. it will be positive
pick a number greater than 5 and test, it will be negative

btw i hope it is clear than saying something is < 0 is the same as saying "negative"

Answer 19

thanks a bizillion