Absolute Value Equations

When solving an absolute value equation, understand that the value of the “inside” of the absolute value symbol may be positive or negative ... once the absolute value is evaluated the result is always positive.  In other words,  or .

Solve the equation: , then  or  .  Solving these equations we would find that  or .  The absolute value equation has two points that satisfy the equation.  Checking this answer would provide the following information:    and .
The solution to the equation is the set {-1,4}.

General Algebra Tips

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This page was edited on 09-Jan-2014