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There can be no solution to an algebra equation because of limitations of the domain. For example,

  • x+3 = 2 has no solution if the domain for x is the set of positive integers,
  • x*3 = 2 has no solution if the domain for x is the set of whole numbers,
  • x^3 = 2 has no solution if the domain for x is the set of rational numbers,
  • x^2 = -2 has no solution if the domain for x is the set of real numbers.

Alternatively, the equation has no solution if it can be reduced to a false statement. For example,

x + 2 = x + 3 can be simplified to 2 = 3 which is false and so there is no solution.

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Q: What is no solution in an algebra equation?
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