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Chapter 1: Equations and Inequalities

Chapter 1: Equations and Inequalities. Lesson 4: Solving Absolute Value Equations. Absolute Value. Absolute Value: of a number is its distance from 0 on the number line. The distance is always nonnegative How far is -5 from 0?. Absolute Value.

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Chapter 1: Equations and Inequalities

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  1. Chapter 1: Equations and Inequalities Lesson 4: Solving Absolute Value Equations

  2. Absolute Value • Absolute Value: of a number is its distance from 0 on the number line. • The distance is always nonnegative • How far is -5 from 0?

  3. Absolute Value • The symbol lxI represents the absolute value of a number • For any real number a, if a is positive or 0 the abs value of a is a. If a is negative, the abs value of a is the opposite of a. • IaI = a, if a ≥ 0, and IaI = -a if a < 0.

  4. Example 1: • Evaluate: 1.4 + I5y - 7I if y = -3 • 1.4 + I5y-7I = 1.4 + I5 (-3) -7I replace y w/ -3 • = 1.4 + I-15 - 7I simplify 5 (-3) first • = 1.4 + I-22I Subtract 7 from -15 • = 1.4 + 22 I-22I = 22 • = 23.4 add • See example #2

  5. Note: • The absolute value is always positive. • So the solution for the equation IxI = -5 is an empty set or ø • See examples

  6. Homework: Pg. 30, #15-47 odd • Classwork: Pg. 29, #1-14

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