How to Determine if an Equation Is an Identity?

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A mathematical equation can be a contradiction, an identity, or a conditional equation. An identity is an equation where all real numbers are possible solutions for the variable. You can verify simple identities such as x=x easily, but more complex equations are more difficult to verify. The easiest way to tell whether or not any equation is an identity is by graphing the difference of both sides of the equation.

    Use the "Graph" function on your graphing calculator. The "Y=" button opens the graphing function on most calculators. To find how to graph using your calculator, consult the owner's manual.

    Enter the left side of the equation into the first "Y=" line. For example, if you have the equation 5(x-3)=5x-15, you would enter "5(x-3)" into the first line.

    Enter the right side of the equation into the second "Y=" line. In the example, you would enter "5x-15."

    Enter "Y1-Y2+1" into the third "Y=" line.

    Graph the 3 equations you entered. If the equation is an identity, the graph for "Y3" will be a horizontal line located at "Y=1." This works because the two sides of an identity equation are equal for all real numbers, so subtracting them will always equal zero. Adding one to the difference makes the horizontal line easier to distinguish from the x axis.