# 1140 L6 - Lecture 6, Part I: Section A.6 Linear...

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Lecture 6, Part I: Section A.6 Linear Inequalities An inequality is a statement that two quantities are not equal. To solve an inequality is to ±nd all values of x that makes that the inequality true. Unlike equations, most inequality usually have an in±nite number of solutions. To present the solution, we use interval notation . Properties of Inequalities Let a , b , c and d be real numbers. 1. Transitive Property If a < b and b < c , then 2. Addition of Inequalities If a < b and c < d , then 3. Addition/Subtraction of a Constant If a < b , then 4. Multiplication/Division by a Constant For c > 0: If a < b , then For c < 0: If a < b , then

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NOTE: To multiply or divide both sides of an inequality by a negative number, reverse the inequality. ex. Solve the inequalities: 1) 2 5 x + 1 < 1 5 ± 2 x 2) ± 1 < 3 2 (2 ± x ) ² 3
Inequalities Involving Absolute Value Recall: j x j is the distance from x to 0 on the number line. ex. Solve: 1) j x j < 1 2) j x j > 1 three-part inequality compound inequality To Solve an Absolute Value Inequality If a

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## This note was uploaded on 07/08/2011 for the course MAC 1140 taught by Professor Williamson during the Spring '08 term at University of Florida.

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1140 L6 - Lecture 6, Part I: Section A.6 Linear...

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