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18 Feb 2021, 04:58
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ibra10
hello VeritasKarishma chetan2u
why do we have to rewrite modulus as in the highlighted part above , i thought transition points should be when modulus equals zero in this case i.e -4 and 2 
19 Feb 2021, 04:03
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dave13
You are right. We don't "have to". The solution just elaborates so that all readers understand what is going on. If we have |x - a| then a is the transition point. So when we have |x + a|, the transition point is given by |x - (-a)| i.e. it is -a.
Note that GMAT anyway only cares about the answer so if you can do it all in your mind, its even better. The better you understand the concept, the fewer steps you will need.
15 Dec 2022, 22:20
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Asked: If |x + 1| = 2|x - 1|, what is the sum of the roots?
|x + 1| = 2|x - 1|
Case 1: x >=1
|x + 1| = x + 1 = 2|x - 1| = 2x - 2
x = 3
Case 2: -1<=x<1
|x + 1| = x + 1 = 2|x - 1| = 2- 2x
3x = 1
x = 1/3
Case 3: x<-1
|x + 1| = -x - 1 = 2|x - 1| = 2- 2x
x = 3: Invalid
Sum of roots = 3 + 1/3 = 10/3
IMO E
|x + 1| = 2|x - 1|
Case 1: x >=1
|x + 1| = x + 1 = 2|x - 1| = 2x - 2
x = 3
Case 2: -1<=x<1
|x + 1| = x + 1 = 2|x - 1| = 2- 2x
3x = 1
x = 1/3
Case 3: x<-1
|x + 1| = -x - 1 = 2|x - 1| = 2- 2x
x = 3: Invalid
Sum of roots = 3 + 1/3 = 10/3
IMO E
