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The number of solutions of the equation |2x − 1| = 3[x] + 2{x} where [x] is the greatest integer ≤ x and {x} is the fractional part of x is

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The number of solutions of the equation |2x − 1| = 3[x] + 2{x} where [x] is the greatest integer ≤ x and {x} is the fractional part of x is 

(1) one 

(2) two 

(3) three 

(4) nil

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1 Answer

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Best answer

Correct option (1) one

Explanation:

If x is negative, RHS is negative, but the LHS is non-negative.

∴ the equation reducesto 1 − 2x = 2x

⇒ x = 1 4

The number of solutions for the given equation is 1.

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