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If [x] is the integral part of a real nu...

If `[x]` is the integral part of a real number `x`. Then solve `[2x]-[x+1]=2x`

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Verified by Experts

The correct Answer is:
`x_(1)=-1,x_(2)=-1//2`
We have `[2x]-[x+1]=2x`
Since LHS`=` Integer
`:.` RHS `=2x=` Integer
`implies[2x]=2x`
Now `-[x+1]=0`
`implies[x+1]=0`
or `0lex+1lt1`
or `-1lexlt0`
or `-2xle2xlt0`
`:.2x=-2,-1`
or `x=-1, -1/2`
or `x_(1)=-1,x_(2)=-1/2`
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