Question

# The number of solutions of the equation $$[x] +2 \{-x\} = 3x$$, is (where [ ] represents the greatest integer function and {x} denotes the fractional part of x)

A
1
B
2
C
3
D
0

Solution

## The correct option is C $$3$$we know that $$1-\left \{ x \right \} = \left \{ -x \right \}$$So,$$x-\left \{ x \right \} + 2\left \{ x \right \} +2= 3x$$$$\left \{ x \right \} +2= 2x$$$$\left \{ x \right \}+2 = 2\left \{ x \right \} + 2[x]$$$$\left \{ x \right \} +2[x]=2$$hence only one solution Maths

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