Solve : `4{x}= x+ [x]`(where `[*]` denotes the greatest integer function and `{*}` denotes the fractional part function.

Explanation

To solve the equation \( 4\{x\} = x + [x] \), where \(\{x\}\) denotes the fractional part of \(x\) and \([x]\) denotes the greatest integer function, we can follow these steps:

### Step 1: Understand the Definitions
The fractional part of \(x\) is defined as:
\[ \{x\} = x - [x] \]
where \([x]\) is the greatest integer less than or equal to \(x\).
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