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Breaking a long overdue

**#Problem 15**
Find the total number of solutions of | [x] - 2x |=4.
(a)1,(b)2,(c)4,(d)6,(e)None of these [Where [x] is Greatest Int Func]
**Solution scheme and approach:**
Case 1** :**( x is a whole number)
so [x]=x
=>|-x|=4 =>x=4 or x=-4
Case 2: ( x is a fraction)
so x=a+f (f is the fractional portion)
then the equation gets converted into
|a-(2a+2f)|=4
=>|-a-2f|=4
=>a=4-2f =>a=3 (when f=1/2) =>x=3.5
or a=-4-2f =>a=-5(when f=1/2)=>x=-4.5
Total four solutions.
Hence option (c)

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