How to tell how many solutions an equation has?

Linear equations in one variable can have no solutions, solutions that are the set of all real numbers (infinite), or one solution. To identify the number of solutions, first, simplify the equation. Then, determine if it follows one of the proceeding forms, which are x=a, a=a, and a=b. These forms have a specific amount of solutions.

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When dealing with linear equations in one variable, consider the type of equation it is and what it is saying about the value of the variable in order to determine the number of solutions it has. Note that linear equations, with real numbers, can have a single solution, an infinite amount of solutions, or no solutions.

First, you may have an equation that takes, when simplified, the following form: x=a, where x is the variable and a is a number. This equation is saying that the value of x is a number. Equations like this have one solution because the variable has a unique value. Moreover, the equation is consistent.

Second, you may have an equation that takes, when simplified, the following form: a=a, where a is a number. This equation is saying that any value of the variable renders the equation true. Equations like this have an infinite number of solutions because any number chosen will render the equation true. In this case, the equation is consistent.

Third, you may have an equation that takes, when simplified, the following form: a=b, where a and b are not the same numbers. This equation is saying that there exists no value for the variable that can render the equation true. Equations like this have no solutions because they are contradictory and inconsistent.

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