2-8 Solving Absolute-Value Equations and Inequalities

150 Chapter 2 Linear FunctionsA compound statement is made up of more than one equation or disjunction is a compound statement that uses the word or. { n n { Disjunction: x -3 OR x > 2 Set builder notation: x|x -3 x > 2 A disjunction is true if and only if at least one of its parts is conjunction is a compound statement that uses the word and. { n n { Conjunction: x -3 AND x < 2 Set builder notation: x|x -3 x < 2 A conjunction is true if and only if all of its parts are true. Conjunctions can be written as a single statement as shown. x -3 and x < 2 -3 x < 21 EXAMPLE Solving Compound InequalitiesSolve each compound inequality. Then graph the solution x + 3 2 OR 3x > 9 Solve both Inequalities for + 3 2 or 3x > 9 x -1 x > 3 The solution set is all points that satisfy x | x -1 or x > 3 . { n n { (- , -1] (3, )B -2x < 8 AND x - 3 2 Solve both Inequalities for < 8 and x - 3 2 x > -4 x 5 The solution set is the set of points that satisfy both x > -4 and x 5, x | x - 4 < x 5 { n n { (-4, 5] 2-8 Solving Absolute-Value Equations and InequalitiesObjectivesSolve compound and solve Absolute-Value Equations and valueWho uses this?))}}}}}}}}

152 Chapter 2 Linear Functions EXAMPLE 2 Solving Absolute-Value Equations Solve each equation. A ⎪x-7⎥ = 5 This can be read as “the distance from x to 7 is 5.” x - 7 = 5 or x - 7 = -5 Rewrite the absolute value as a disjunction. x = 12 or x = 2 Add 7 to both sides of each equation. B ⎪3x⎥ + 5 = 14 ⎪3x⎥ = 9 Isolate the absolute-value expression. 3x = 9 or 3x = -9 Rewrite the ...

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  Value, Solving, Equations, Inequalities, Absolute, Absolute value, Solving absolute value equations and inequalities, Value equations

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