x is the variable (because it changes depending on the conditions - it varies).

`x-3/5 = 1- x/3`

Simplify the equation by removing the denominator:

LCD (lowest common denominator) is 15 (3x5 is the lowest):

`15(x) - 15(3/5) = 15 (1) - 15 (x/3)`

Note how the 15 cancels out the denominator in the `3/5 and x/5`

`therefore 15x - 9 = 15 - 5x`

Now solve:

15x + 5x = 15 + 9 (note the symbols)

`therefore 20x = 24`

`therefore x = 24/20`

Simplify (4 will go into both numerator and denominator):

`therefore x= 6/5 or 1 1/5`

Now to check, substitute the answer into your original equation:

`6/5 - 3/5 = 1- (6/5)/3`

It is difficult to understand the fraction which can therefore be written in a different format:

`3/5= 1- (6/5 divide 3)`

`3/5 = 1- (6/5 times 1/3)`

`3/5= 1 - 2/5`

`therefore 3/5=3/5`

`x= 6/5 or 1 1/5`

`therefore` **x= 6/5 or 1 1/5**