Question

| x -1| -2 =| 2x -5 | solve

Answer 1

please help me

Answer 2

there are two things to remember when dealing with absolute values
that the x can be less than zero or greater than zero
meaning you would have either a positive value for it or a negative value for it.

Answer 3

make 4 cases of x>=1 x<1, x>=5/2, x<5/2

Answer 4

and I solve for x ??

Answer 5

naturally, that is what you do :D

Answer 6

can you just give me the first equation plz

Answer 7

Guys !1

Answer 8

ok, we use the simple fact that when |a|=b ,
either a=b or a=-b

we need to use that twice here, because we have |....| twice.

so see this example :
|a|+b=|c| gives 2 equations,
(|a|+b=c) or (|a|+b=-c)
which again gets split to 4 equations,
(a+b=c or -a+b=c) or (a+b=-c or -a+b=-c)

read this carefully and tell me whether u get it...

Answer 9

ask if u have any doubt in any step.

Answer 10

ok I'll do my best

Answer 11

nice work @hartnn

Answer 12

hey thanks :)

Answer 13

so @hataki lets first split this into 2 equations,
| x -1| -2 =| 2x -5 |

which 2 equations ?

Answer 14

| x -1| -2 =| 2x -5 | or | x -1| -2 = -| 2x -5 |
right ?

Answer 15

when you have splitted, no need to use |...| again!
so its
| x -1| -2 = 2x -5 or | x -1| -2 = -( 2x -5 )

ok ?

Answer 16

ok get it and now we split them into 4 equations

Answer 17

yes, the idea is same and simple., |a| = b gives a=b or a=-b

so, lets first only take 1st equation and split it into 2
| x -1| -2 = 2x -5
2 equations ?

(if you are confident, write all 4 equations :))

Answer 18

1) x-1-2=2x-5
2) -x+1-2=2x-5
3)x-1-2=-(2x-5)
4)-x+1-2=-(2x-5)
right ??

Answer 19

oh, wow , absolutely correct! :)
you learn fast.

Answer 20

just solve them individually and get 4 values of x first....they are simple algebraic equations with no twists now...

Answer 21

THANK YOU SO SO SO MUCH :D
if I messed up can I get back to you ??

Answer 22

ANd thanks to every one :D

Answer 23

sure, please tell us what you get finally, we will verify it!
also, its not always necessary that all 4 values are solution, we need to cross verify, so you better tell us what 4 values u get, then we will proceed on verification

Answer 24

ok I'm work on them NOW :D

Answer 25

1) x=2
2) x=4/3
3) x=8/3
4) x=6

Answer 26

all correct! :)

Answer 27

now we put these one by on in original equation!
put x=2 in | x -1| -2 =| 2x -5 |
|1| -2 = |-1|
so, 1 - 2 = 1
which is false! so, x= 2 is not the solution, got this ?

Answer 28

yeah I'm working on them :D

Answer 29

sir non of them worked
they all not equal

Answer 30

thats absolutely correct!
there is actually no solution to your original equation :)

Answer 31

thank you so much sir I do understand it now :D :D

Answer 32

you are welcome ^_^