Question

Solve:
-|2m-1| < 2
and please explain how to solve it.

Answer 1

|f(x)|<y

->

-y < f(x) < y

Answer 2

|f(x)| > y

->

f(x) > y , f(x) < -y

Answer 3

can you do it now ?

Answer 4

um, no, I don't get what you mean by all that..

Answer 5

ok if we divide the equation by -1 what will we get ?

Answer 6

well, my teacher said to change the < to a = when I solve these types of problems so i would get:
|2m-1| = -2

Answer 7

ok if you want to do it this way you dont have to divide.. but if you done it already
now you know to find m's that satisfy |2m-1| = -2 ?

Answer 8

well, to get rid of the absolute values first, I just seperated it into 2m -1 = -2 and 2m -1 = 2 like my teacher told me to and I got the answers -1/2 and 3/2 but when I tried to check it, it doesn't seem right..

Answer 9

you have to plug now some m<-1/2 like m = -1
-1/2 < m < 3/2 lke m = 1
and m>3/2 like m = 2
in the original equation and see if it holds

Answer 10

when does it hold?

Answer 11

are you there?

Answer 12

yeah sorry, I tried numbers but it didn't work...

Answer 13

can someone else tell me how to solve this or if I'm doing something wrong?

Answer 14

why? when you plug m=-1
what do you get?

Answer 15

i get -4 <2

Answer 16

so it holds isnt it?

Answer 17

-4 is indeed smaller than 2

Answer 18

yes, I know but the answers i got for m and every other number works too which shouldn't be happening

Answer 19

it works for every m

Answer 20

it is obvious.. the original question is negative number < 2
so it always holds

i wanted to work on the technique with you

Answer 21

i don't get how that can work though...so the answer is that all numbers work?

Answer 22

yes it is obvious ..
all the negative numbers are smaller than 2

Answer 23

if you didnt see it at the original question you could see it when you asked yourself
|2m-1| = -2
?
it is never happens .. since left hand side of the equation is always positive !!

Answer 24

ohhhh, okay, thank you :)

Answer 25

yw;)