JEE Class main Answered

|x-2|+|x-5| = 3  .......................... (1)

Let (x-2) > 0 and (x-5)>0 , then we have

(x-2)+(x-5) = 3

2x = 10  or  x = 5

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Let (x-2) < 0 and (x-5) < 0 , then we have

(2-x)+(5-x) = 3

7-2x = 3  or  x = 2

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Hence solution to the equation (1) is x= 2 or x= 5