Find the number of solutions of `abs([x]-2x)=4`, where [x] is the greatest integer ` le ` x.

Options

A. infinite
B. 4
C. 3
D. 2

Answer

A

Explanation

We have `|[x]-2x|=4`
`implies|[x]-2([x]+{x})|=4`
`implies|[x]+2{x}|=4`
which is possible only when
`2{x}=0,1`
If `{x}=0 then `[x]=+-4` and then `x=-4,4` and if `{x}=1/2`, then
`[x]+1=+-4`
`implies[x]=3,-5`
`:.x=3+1/2` and `-5+1/2`
`impliesx=7/2,-9/2impliesx=-4, -9/2,7/2,4`