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X = 1  is an equation, it can also be written as  x  - 1 = 0 , it is an equation of first degree in x.

 x = x + 5 is not an equation.  it is not valid, as   it reduces to  0 = 5.  

1 5 1
X=1 is a equation and x=x+5 is not an equation.
1 3 1