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Precalc0011to0016-page12 - ± ”(is less than or equal to...

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(Section 0.12: Solving Inequalities) 0.12.1 SECTION 0.12: SOLVING INEQUALITIES LEARNING OBJECTIVES • Know how to solve linear inequalities and absolute value inequalities. PART A: DISCUSSION • We will solve inequalities when we perform sign analyses and find domains of radical functions (see Sections 1.1 and 2.11). Absolute value inequalities allow us to write more compact statements, particularly with respect to distances on the real number line. • We will solve nonlinear inequalities in Section 2.11. PART B: SOLVING LINEAR INEQUALITIES Strict inequalities involve the “ < ” (is less than) or the “ > ” (is greater than) signs. Weak inequalities involve the “
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Unformatted text preview: ± ” (is less than or equal to) or the “ ± ” (is greater than or equal to) signs. Inequations involve the “ ± ” (is not equal to) sign. Solving linear inequalities is similar to solving linear equations , but with the following differences: • Typically, an inequality has infinitely many solutions , and the solution set is often written in interval form . • WARNING 1 : We must reverse the direction of the inequality sign if we switch the sides of an inequality, or if we multiply or divide both sides by a negative number. Solving inequations is also similar to solving equations, although “ ± ” never needs to be reversed....
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