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)
=>|-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=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)