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# Topic 16 - the variable You can apply the definition to...

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*ABSOLUTE VALUE EQUATIONS AND INEQUALITIES* You learned how to find the absolute value of a number long ago. In this topic you deepened your understanding of the absolute value function by exploring its graph. You can think of the graph as pieces of two different linear functions. The graph gives you a visual representation of the definition of absolute value: As you have seen in the examples, a may represent a number, a single variable, or a longer expression involving numbers and variables. ** If this seems complicated, learn the definition in words and repeat it as you use it: If the expression is positive or zero, the absolute value is the same expression; and if the expression is negative, the absolute value is the opposite of the expression. This definition is the key to dealing with the absolute value of an expression containing a variable. Such an expression may be positive, zero, or negative depending on the value of

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Unformatted text preview: the variable. You can apply the definition to split an absolute value expression into two parts that are easier to handle. You should know how to use the definition to replace the absolute value of an expression in order to solve equations and inequalities. Replacing the absolute value results in two equations or inequalities, each with different domains. These are solved in the ways you have learned. ***The solution set of an absolute value equation usually contains two numbers. The solution set of an absolute value inequality usually consists of two inequalities connected with "or" if the solutions do not overlap and connected with "and" if they do overlap. or or and It is possible for the solution set to be the empty set or to contain all real numbers. No solution Solution set: all real numbers...
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Topic 16 - the variable You can apply the definition to...

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