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Definition of Absolute Value “Absolute value” means “distance away from zero” on a number line Distance is always positive or zero Absolute value is indicated by placing vertical parallel bars on either side of a number or expression Examples: The distance away from zero of -3 is shown as: The distance away from zero of 3 is shown as: The distance away from zero of u is shown as: = u

Absolute Value Equation An equation that has a variable contained within absolute value symbols Examples: | 2x – 3 | + 6 = 11 | x – 8 | – | 7x + 4 | = 0 | 3x | + 4 = 0

Solving Absolute Value Equations Isolate one absolute value that contains an algebraic expression, | u | If the other side is negative there is no solution (distance can’t be negative) If the other side is zero, then write: u = 0 and Solve If the other side is “positive n”, then write: u = n OR u = - n and Solve If the other side is another absolute value expression, | v |, then write: u = v OR u = - v and Solve

Example of Solving Absolute Value Equation

Example of Solving Absolute Value Equation

Example of Solving Absolute Value Equation

Example 1 Evaluate an Expression with Absolute Value Example 2 Solve an Absolute Value Equation Example 3 No Solution Example 4 One Solution Lesson 4 Contents

Evaluate Replace x with 4. Simplify –2(4) first. Subtract 8 from 6. Add. Answer: The value is 4.7. Example 4-1a

Evaluate Answer: –13.7 Example 4-1b

Solve Check your solutions. Case 1 or Case 2 Check: Answer: The solutions are 5 or –11. Thus, the solution set is Example 4-2a

Solve Check your solutions. Answer: Example 4-2b

Subtract 5 from each side. Solve Original equation Subtract 5 from each side. This sentence is never true. Answer: The solution set is . Example 4-3a

Solve Answer:  Example 4-3b

Solve Check your solutions. Case 1 or Case 2 There appear to be two solutions, 11 or Example 4-4a

Answer: Since , the only solution is 11. The solution set is {11}. Check: Answer: Since , the only solution is 11. The solution set is {11}. Example 4-4b

Solve Answer: {6} Example 4-4c

End of Lesson 4

Homework Pages 30 – 31 #’s 18 – 26, 29 – 40 Due Tomorrow (9/9/09)