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L06 - Lecture 6 Part I Section A.6 Linear Inequalities An...

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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 find all values of u1D465 that makes that the inequality true. Unlike equations, most inequality usually have an infinite number of solutions. To present the solution, we use interval notation . Properties of Inequalities Let u1D44E , u1D44F , u1D450 and u1D451 be real numbers. 1. Transitive Property If u1D44E<u1D44F and u1D44F<u1D450 , then 2. Addition of Inequalities If u1D44E<u1D44F and u1D450<u1D451 , then 3. Addition/Subtraction of a Constant If u1D44E<u1D44F , then 4. Multiplication/Division by a Constant For u1D450> 0: If u1D44E<u1D44F , then For u1D450< 0: If u1D44E<u1D44F , 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 u1D465 + 1 < 1 5 2 u1D465 2) 1 < 3 2 (2 u1D465 ) 3
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Inequalities Involving Absolute Value Recall: u1D465 is the distance from u1D465 to 0 on the number line.
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