Question

Find the value of k that makes the inequality
2kx-3k<2x+4+3kx
have no solution.

Answer 1

@adamaero You are the first person to at least look -_-, thanks

Answer 2

Did you try plugging in numbers?

Answer 3

yeah, but i get stuck with the x
for instance, when I plugged in 1, I got
-3x<7

Answer 4

So far, all I could simplify the equation to is -kx-3k<2x-4

Answer 5

did you try solving for x

Answer 6

No, because k will be in the way

Answer 7

and then look at the domain restrictions for k afterwards

Answer 8

put all of your x's on onside and all your things that don't have x in it on the other

Answer 9

let me know when you have done this

Answer 10

;-;

Answer 11

\[2kx-3k<2x+4+3kx \\ \text{ subtracting } 3kx \text{ on both sides } \\ -kx-3k<2x+4\]
how did your 4 end up being -4 ?

Answer 12

It didn't, sorry, copied it wrong.

Answer 13

ok well we are attempting to isolate x
we need to subtract 2x on both sides and add 3k on both sides

Answer 14

that wont do much...

Answer 15

but contine

Answer 16

*continue

Answer 17

\[-kx-2x<3k+4 \\ x(-k-2)<3k+4 \\ \text{ if } -k-2>0 \text{ then } x<\frac{3k+4}{-k-2} \\ \\ \text{ if } -k-2<0 \text{ then } x> \frac{3k+4}{-k-2}\]
anyways in either inequality k cannot be...

Answer 18

oh i see, so you could factor x

Answer 19

yep that is why I asked you to put all your x terms on one side and terms without x on the other side

Answer 20

however, I can't find k while x itself is still an inequality.

Answer 21

? you do know you cannot divide by 0 right?

Answer 22

so k cannot be

Answer 23

-k-2 is zero when k is?

Answer 24

however is k was zero, 0-2 is negative two, which you can divide by

Answer 25

2

Answer 26

well if k=-2 then -k-2 is 0

Answer 27

oh xD

Answer 28

see what happens when you plug it into your original inequality

Answer 29

oh, that makes sense!

Answer 30

the inequality will definitely not have a solution when k=-2
\[2(-2)x-3(-2)<2x+4+3(-2)x \\ -4x+6<2x+4-6x \\ -4x+6<-4x+4\]

Answer 31

plus to both sides 4x
then 6 is not greater than 4

Answer 32

solve the inequality for when k=-2
you will see great fail

Answer 33

great

Answer 34

TYVM

Answer 35

np

Answer 36

one more thing ...

Answer 37

if the inequality was switched
they might have asked for which k does the inequality hold for all x

Answer 38

because you would have winded up with 6>4

Answer 39

which would be try for all x

Answer 40

just for fun I thought I would mention that

Answer 41

so it was an all or none situation

Answer 42

if that makes sense

Answer 43

true* not try