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An equation is an assertion that two mathematical expressions are equal as in:

  • left-hand-side = right-hand-side

The equality can be justified because

  1. the statement is a Mathematical identity or
  2. the statement is a Mathematical definition or
  3. the statement describes the relationship between two or more expressions.

The equation

  • a + b = b + a

is justified because the addition operation is commutative. This equation is the symbolic equivalent of that property. On the other hand, the equation

  • y = a + b x

is an assertion about the symbols it mentions.

  1. Letters from the beginning of the alphabet like a, b, ... are convenctionally considered as constants in the context of the discussion at hand.
  2. Letters from end of the alphabet, x,y,z are usually considered variables, that is, their values may change within the discussion.
See Linear equations, Quadratic equation