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

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Solve : `4{x}= x+ [x]`(where `[*]` denotes the greatest integer function and `{*}` denotes the fractional part function.
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We have `4{x} = x + [x]`
or `" "4{x}= x+ x- {x}`
or `" "5{x}= 2x `
or `" "{x}= (2x)/(5)`
Now draw the graphs of `y= {x} and y= (2)/(5)x`.
image
From the graph, one of the solutions is `x=0`.
Other solution occurs where `(2)/(5)x= x-1 `
or `" "x= (5)/(3)`
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