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?
+LHS = +RHS
-LHS = -LHS
-LHS = +RHS
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:
Ques3.jpg [ 6.93 KiB | Viewed 889 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/
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