-
vittalgmat
- Legendary Member
- Posts: 621
- Joined: Wed Apr 09, 2008 7:13 pm
- Thanked: 33 times
- Followed by:4 members
Hi,
I would like the experts to weigh in on this. (Ron, Ian, Stuart, Stacey??)
I will ask my question first.
What method is applicable to what class of problems?
As I understand, there are two ways to algebraically solve absolute equations (apart from the conceptual distance numberline method). The following are the two ways I found.
Method 1) Whenever u see problem of the type
Is |x| < 1 ?
(1) |x + 1| = 2|x - 1|
Solving the two cases a) (x +1 ) = 2(x-1) and
b) (x +1) = - 2(x -1)
are sufficient.
Ref: see Ron Purewal's explanation here:
https://www.manhattangmat.com/forums/abs ... t3648.html
Method 2) For solving problems of the type, we need to use a critical point approach
If y = /x + 7/ + /2 - x/, is y = 9?
(1) x < 2
(2) x > -7
(Ref: see the MGMAT Tutorial on Absolute values Slide 61
https://www.manhattangmat.com/tutorials/ ... -value.cfm )
The critical point approach is illustrated in the same tutorial. This link below also explains the critical point approach but as Ron mentioned, critical point approach is a overkill for that problem in the link below. It could have been solved by Method 1.
https://www.beatthegmat.com/tricky-inequ ... 22180.html
Thank you very much
I would like the experts to weigh in on this. (Ron, Ian, Stuart, Stacey??)
I will ask my question first.
What method is applicable to what class of problems?
As I understand, there are two ways to algebraically solve absolute equations (apart from the conceptual distance numberline method). The following are the two ways I found.
Method 1) Whenever u see problem of the type
Is |x| < 1 ?
(1) |x + 1| = 2|x - 1|
Solving the two cases a) (x +1 ) = 2(x-1) and
b) (x +1) = - 2(x -1)
are sufficient.
Ref: see Ron Purewal's explanation here:
https://www.manhattangmat.com/forums/abs ... t3648.html
Method 2) For solving problems of the type, we need to use a critical point approach
If y = /x + 7/ + /2 - x/, is y = 9?
(1) x < 2
(2) x > -7
(Ref: see the MGMAT Tutorial on Absolute values Slide 61
https://www.manhattangmat.com/tutorials/ ... -value.cfm )
The critical point approach is illustrated in the same tutorial. This link below also explains the critical point approach but as Ron mentioned, critical point approach is a overkill for that problem in the link below. It could have been solved by Method 1.
https://www.beatthegmat.com/tricky-inequ ... 22180.html
Thank you very much
