Algebra , Polynomials

Algebra Level 2

How many real numbers x are solutions to the following equation?

∣ x − 1 ∣ = ∣ x − 2 ∣ + ∣ x − 3 ∣ |x-1|=|x-2|+|x-3|

2 6 3 4

Ankit Vijay by Ankit Vijay , 22, India

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2 solutions

Pradeepa Bk
Jun 25, 2014

Draw |x-1| and [x-2|+|x-3| on graph, we can notice only two intersections

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Anoir Trabelsi
Jun 4, 2014

Try to square both sides and then consider two cases ( whether the expression inside the absolute value is positive or negative) you'll find that the solutions are x=2 and x=4 . Therefore the answer is 2 .

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