## xRAWRRx3 3 years ago Solve: -|2m-1| < 2 and please explain how to solve it.

1. Coolsector

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

2. Coolsector

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

3. Coolsector

can you do it now ?

4. xRAWRRx3

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

5. Coolsector

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

6. xRAWRRx3

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

7. Coolsector

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 ?

8. xRAWRRx3

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..

9. Coolsector

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

10. Coolsector

when does it hold?

11. Coolsector

are you there?

12. xRAWRRx3

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

13. xRAWRRx3

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

14. Coolsector

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

15. xRAWRRx3

i get -4 <2

16. Coolsector

so it holds isnt it?

17. Coolsector

-4 is indeed smaller than 2

18. xRAWRRx3

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

19. Coolsector

it works for every m

20. Coolsector

it is obvious.. the original question is negative number < 2 so it always holds i wanted to work on the technique with you

21. xRAWRRx3

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

22. Coolsector

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

23. Coolsector

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 !!

24. xRAWRRx3

ohhhh, okay, thank you :)

25. Coolsector

yw;)