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Solving Absolute Value Equations

• The absolute value of a number is its distance from 0.

• The absolute value of x is equal to x if x is greater than or equal to 0; otherwise, it is equal to –x.

• Use this definition of absolute value to solve equations involving absolute values. Split the original equation |x| = a into two different possibilities, or cases, based on the definition: x = a and x = --a. Solve each one and combine the solutions.

• Some equations have no solutions.

• Always check all of the solutions. Some may not satisfy the original equation and must be discarded.