Special Cases: Identities and No Solutions

An equation has no solution if no value of the variable makes the equation true. The equation 2x = 2x + 1 has no solution. An equation that is true for every value of the variable is an identity. The equation 2x = 2x is an identity.

Identities and Equations with No Solutions

a. Solve 10 – 8a = 2(5 – 4a).

b. Solve 6m – 5 = 7m + 7 – m.

Check Understanding

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Interactivity Use the interactivity to learn how to graph each side of an equation, and how to identify which equations have 1 solution, no solutions, and infinitely many solutions.

Exercises Click here to view the Exercises for this lesson.

Technology Click here to view Technology: Graphing Equations.

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