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Linear Functions

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SSection 8: Solving Absolute-Value Equations and Inequalities

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SSolve compound inequalities. WWrite and solve absolute value equations and inequalities.

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ddisjunction cconjunction aabsolute value

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AAbsolute value can be used to represent the acceptable ranges for the dimensions of baseball bats classified by length or weight. (See Exercise 43.)

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AA compound statement is made up of more than one equation or inequality. AA disjunction is a compound statement that uses the word or. AA conjunction is a compound statement that uses the word and.

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RRecall that the absolute value of a number x, written |x|, is the distance from x to zero on the number line. BBecause absolute value represents distance without regard to direction, the absolute value of any real number is nonnegative.

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AAbsolute-value equations and inequalities can be represented by compound statements. CConsider the equation |x| = 3. TThe solutions of |x| = 3 are the two points that are 3 units from zero. The solution is a disjunction: x = -3 or x = 3.

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TThe solutions of |x| < 3 are the points that are less than 3 units from zero. The solution is a conjunction: -3 < x < 3. TThe solutions of |x| > 3 are the points that are more than 3 units from zero. The solution is a disjunction: x < -3 or x > 3.

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Note: The symbol ≤ can replace <, and the rules still apply. The symbol ≥ can replace >, and the rules still apply.

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You can solve absolute-value inequalities using the same methods that are used to solve an absolute-value equation. Solving an Absolute

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PPage 154 11-35

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