Question

inequality question - equation inside; PLEASE HELP!

Answer 1

\[\frac{ x + 5 }{ 4x } > 3\]

Answer 2

solve for x

Answer 3

these are tricky.

start with
\[ \frac{ x + 5 }{ 4x } -3 > 0\]

Answer 4

okay... then what D:

Answer 5

use a common denominator of 4x to change 3 to 12x/4x
and subtract the two fractions. Can you do that ?

Answer 6

you lost me.

Answer 7

wait.... i got it

Answer 8

nevermind. i'm lost.

Answer 9

\[ \frac{ x + 5 }{ 4x } -3 > 0 \\ \frac{ x + 5 }{ 4x } +\frac{-3\cdot 4x}{4x} > 0 \]

when you have two fractions with the same denominator, you can add or subtract their tops, and put that result over the common denominator.

Answer 10

so then you get -11x + 5...all that over 4x?

Answer 11

i don't think anything can confuse me more than inequalities and stupid fractions.

Answer 12

yes,
\[ \frac{-11x + 5}{4x} > 0\]

now you need to use this idea: a fraction A/B > 0 means A/B is a positive number. A/B will be positive if A is positive and B is positive OR both are negative.

Answer 13

well A isn't positive

Answer 14

First Case: both top and bottom are positive. for that to be true we need
-11x+5>0
and (at the same time)
4x > 0
can you solve for x ?

Answer 15

i don't freaking know, i got x < 5/11 and x < 0

Answer 16

i'm angry at myself not you. i'm so frustrated with not understanding this.

Answer 17

let's first do 4x > 0
we can divide both sides by 4
x > 0/4 or x> 0
in other words 4x is positive as long as x is positive.... i.e. x>0

now -11x+5>0

it is *always safer* to add to both sides . add +11x to both sides
-11x + 11x +5 > 11x
5 > 11x
5/11 > x
or x < 5/11

we have
x>0 and x<5/11
which we can write as
0 < x < 5/11

Answer 18

but you said x > 0, 0 < x is this opposite of that isn't it?

Answer 19

the "big side" of > is next to the bigger number
x > 0 (x bigger than zero) is the same thing as 0 < x (0 is less than x)
if x is bigger than 0, then 0 is smaller than x

Answer 20

Second Case: both are negative
-11x+5< 0
and (at the same time)
4x < 0

what do you get for this case ?

Answer 21

okay. thank you. i have two more problems like this so i'm gonna try both of them in the same way this one was done

Answer 22

can you finish this one?

Answer 23

You should get
-11x+5< 0 --> 5/11 < x
4x < 0 -----> x<0
you need both of these to be true at the same time (so we get a negative up top and a negative in the bottom).
but x cannot be both less than 0 and at the same time greater than 5/11
so this case cannot happen.
the final answer is
0 < x < 5/11 (from the first case)

Answer 24

so if i get x < 3/5 and x < 0, would my final answer be 0 < x < 3/5 ?

Answer 25

I assume this is a different question.
But if you need both conditions to be true *at the same time*
x < 3/5 and x < 0
then you need x<0 (if x < 0 then both conditions are satisfied)

Answer 26

yes it is a different question. so would my answer be correct? because x < 0

Answer 27

0 < x < 3/5 is short for x bigger than 0 and smaller than 3/5
(in other words, x is between 0 and 3/5 )
that is not the same as x<0 and x< 3/5

Answer 28

so what the heck am i supposed to put. x < 0 < 3/5 ?

Answer 29

or 3/5 > 0 > x ?

Answer 30

remember, the pointy end (smaller, narrow end) of < is next to the smaller number

***so what the heck am i supposed to put. x < 0 < 3/5***
it would be nice to see the original problem, but what you have found is you need one expression to be x<0 and the other expression to be x<3/5
(to get the correct signs)

you can think of it like this: x<0 (for example x=-1, "works" for -1<3/5)
both expressions will have the correct sign.

but even though x=1/5 works for 1/5< 3/5, it does not work for 1/5 < 0 (no, 0 is smaller than 1/5)

Answer 31

one of my expressions was x < 0 and the other was x < 3/5. it works. my question is how do i write the final answer.

do you want me to post the whole problem? i think i did it right but if you would like to check my work and do it yourself i don't mind posting it.

Answer 32

one of my expressions was x < 0 and the other was x < 3/5

The main idea is that both must be true at the same time.
if we plot them, like this