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Number of solutions of the equation [2x] − 3{2x} = 1 (where [⋅] and {⋅} denotes the greatest integer and fractional part function respectively) is
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    0
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Number of solutions of the equation [2x] − 3{2x} = 1(where [&sdo...
The equation [2x] = 0 has no solutions if x is not an integer or if x is an integer but not within the range of -0.5 to 0.5.

If x is an integer within the range of -0.5 to 0.5, then [2x] = 0. In this case, there are infinitely many solutions.
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Community Answer
Number of solutions of the equation [2x] − 3{2x} = 1(where [&sdo...
Given [2x] − 3{2x} = 1
Let x = I + f, where I is integral part and f is fractional part.

Case-I

From the Case-I

Case-II

Case-III


So, three solutions are 
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Number of solutions of the equation [2x] − 3{2x} = 1(where [⋅]and {⋅}denotes the greatest integer and fractional part function respectively) isa)1b)2c)3d)0Correct answer is option 'C'. Can you explain this answer?
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