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# Absolute Value Equations & Inequalities

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### Absolute Value Equations & Inequalities

1. 1. Agenda Tuesday, Dec. 1 Homework 11 p. 169 # 5 - 8, 10, 12, 16 - 18, 27 - 30, 40 - 44 correct homework Meet me in the computer lab tomorrow Absolute Value Equations & Inequalities Ch. 3 test on Thursday
2. 6. Absolute Value Equations Absolute Value is the distance a number is from zero on a number line. The absolute value of 4 would be at either -4 or +4. If we write this as an equation, x = 4 the two solutions of the equation x = -4 and +4 1 0 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
3. 7. Solving Absolute Value Equations x + 6 = 13 - 6 - 6 x = 7 Using the definition of absolute value x = 7 or x = -7 Check x + 6 = 13 7 + 6 = 13 or -7 + 6 = 13 7 + 6 = 13 or 7 + 6 = 13
4. 9. Some absolute value equations have variable expressions within the absolute value symbol. 4 n - 3 = 9 Write two equations. 4 n - 3 = 9 4 n - 3 = -9 +3 +3 +3 +3 4 n = 12 4 n = -6 n = 3 or n = -1 1/2
5. 11. What is the solution? 3 n = -24 There is No solution - absolute value CANNOT be negative.
6. 12. Absolute Value Inequalities x + 2 < 4 means the expression x + 2 is less than 4 spaces from zero on the number line x + 2 > 4 means the expression x + 2 is greater than 4 spaces from zero on the number line. 1 0 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 1 0 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
7. 13. Solving Absolute Value Inequalities Solve n - 5 < 3, graph the solution. n - 5 < 3 and n - 5 > -3 +5 +5 +5 +5 n < 8 and n > 2 2 < n < 8 1 0 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
8. 14. Solving Absolute Value Inequalities Solve n - 5 > 3, graph the solution. n - 5 > 3 OR n - 5 < -3 +5 +5 +5 +5 n > 8 OR n < 2 1 0 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
9. 17. Attachments