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# How can you tell when an equation in one variable has infinitely many solutions or no solutions?

There is no simple method. The answer depends partly on the variable's domain. For example, 2x = 3 has no solution is x must be an integer, or y^2 = -9 has no solution if y must be a real number but if it can be a complex number, it has 2 solutions. Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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You can actually solve the equation. With some experience with equations, you will eventually know that equations of a certain form will have exactly one solution (for example, a linear equation); while a polynomial equation of degree 2 typically has 2 solutions, and certain types of trigonometric equations have infinitely many solutions (this is due to the periodicity of the trigonometric functions) - but there is really no simple or universal way to tell in advance how many solutions a given equation has.  Earn +20 pts  