Sum of all the values of x satisfying the equation 4{x}=x+[x] where { } and [ ] represent fractional function and greatest integer function respectively.

[x] +{x} = x

Now, coming to our question

4{x}=[x]+x

Substituting the value of x,

4{x}=[x]+[x]+{x}

Subtracting {x} from both sides,

3{x}=2[x]

Dividing both sides by 3,

{x}=2[x] /3

Now, as we know that

0

0

0

So, solution of above is

[x] = 0 or [x] = 1

Case (i) if [x] = 1,

{x} = 2[x] /3

= 2/3

As, x =[x] + {x}

x=1+2/3 =5/3

Case (ii) if [x] =0

{x} =2[x]/3

= 0

As, x = [x] +{x}

x=0+0 =0

So, solutions of

4{x}=[x]+x are x=0 and x = 5/3.