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# Some equations have no solutions in a given number system, but have a solution in a larger system

## Standards derived from the same national standard

Some equations have no solutions in a given number system, but have a solution in a larger system. For example, the solution of 𝘹 + 1 = 0 is an integer, not a whole number; the solution of 2𝘹 + 1 = 0 is a rational number, not an integer; the solutions of 𝘹² – 2 = 0 are real numbers, not rational numbers; and the solutions of 𝘹² + 2 = 0 are complex numbers, not real numbers.

Some equations have no solutions in a given number system, but have a solution in a larger system. For example, the solution of 𝘹 + 1 = 0 is an integer, not a whole number; the solution of 2𝘹 + 1 = 0 is a rational number, not an integer; the solutions of 𝘹² – 2 = 0 are real numbers, not rational numbers; and the solutions of 𝘹² + 2 = 0 are complex numbers, not real numbers.

Some equations have no solutions in a given number system, but have a solution in a larger system. For example, the solution of 𝘹 + 1 = 0 is an integer, not a whole number; the solution of 2𝘹 + 1 = 0 is a rational number, not an integer; the solutions of 𝘹² – 2 = 0 are real numbers, not rational numbers; and the solutions of 𝘹² + 2 = 0 are complex numbers, not real numbers.

Some equations have no solutions in a given number system, but have a solution in a larger system. For example, the solution of 𝑥 + 1 = 0 is an integer, not a whole number; the solution of 2𝑥 + 1 = 0 is a rational number, not an integer; the solutions of 𝑥² – 2 = 0 are real numbers, not rational numbers; and the solutions of 𝑥² + 2 = 0 are complex numbers, not real numbers.

Some equations have no solutions in a given number system, but have a solution in a larger system. For example, the solution of 𝑥 + 1 = 0 is an integer, not a whole number; the solution of 2𝑥 + 1 = 0 is a rational number, not an integer; the solutions of 𝑥² – 2 = 0 are real numbers, not rational numbers; and the solutions of 𝑥² + 2 = 0 are complex numbers, not real numbers.

Some equations have no solutions in a given number system, but have a solution in a larger system. For example, the solution of 𝑥 + 1 = 0 is an integer, not a whole number; the solution of 2𝑥 + 1 = 0 is a rational number, not an integer; the solutions of 𝑥² – 2 = 0 are real numbers, not rational numbers; and the solutions of 𝑥² + 2 = 0 are complex numbers, not real numbers.