Identify what the isolated absolute value is set equal to a. To see why there can be two solutions, you can solve an absolute value equation. Now the key here at first it looks kind of daunting. Let me just rewrite this equation so that the absolute values really pop out. Notice that we have considered two possibilities, both the positive and negative.
Absolute value equations and inequalities absolute value definition the absolute value of x, is defined as. Unless x0, every absolute value equation should have two solutions. An algorithm for solving the absolute value equation. If youre not sure of that solution, graph the two associated absolutevalue functions, and confirm that the two lines intersect at x no graphing calculator. Lets see if we can solve absolute value equations now. We will look at equations with absolute value in them in this section and well look at inequalities in the next section. Has two solutions x a and x a because both numbers are at the distance a from 0. Then solve each equation separately to get two solutions. Solving absolute value equations and inequalities algebra 1. We shall also give a method of solution based on successive linear programming. This is indicated with a disjunction, a mathematical statement created by a connecting two other statements with the word or. Pdf an algorithm for solving the absolute value equation. Absolute value can be positive or negative x7 or x. An extraneous solution is an apparent solution that must be rejected because it does not satisfy the original equation.
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