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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
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B
2
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C
3
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D
0
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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 

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