rohitgoel15 wrote:

Silly doubt

When we solve the below equation , how many possible solutions we have?

|x – 3| = |2x – 3|

Which of the below cases we need to consider when we face such a equation?

Case 1

+LHS = +RHS

Case 2

-LHS = -LHS

Case 3

-LHS = +RHS

Case 4

LHS = -RHS

Or you can forget all cases and do it logically!

|x – 3| means distance from point 3 on the number line.

|2x – 3| = 2|x – 3/2| means twice of distance from 1.5 on number line.

Where will these distances be equal?

It will be at a third of the distance between 1.5 and 3 and also at 1.5 to the left of 1.5 as shown in the two diagrams below:

Attachment:

Ques3.jpg [ 6.93 KiB | Viewed 1018 times ]
i.e. x can take two values 2 and 0.

For more on the theory of mods, check:

http://www.veritasprep.com/blog/2011/01 ... edore-did/http://www.veritasprep.com/blog/2011/01 ... s-part-ii/ _________________

Karishma

Veritas Prep | GMAT Instructor

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