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Absolute Value Equations & Inequalities

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  • 1. Agenda Tuesday,Dec. 1 Homework11p. 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. 3. 4. 5. 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 equationx =-4 and +4 1 0 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 7. Solving Absolute Value Equations x + 6= 13 - 6 - 6 x =7 Using the definition of absolute value x =7orx =-7 Check x + 6 = 13 7 + 6 = 13 or-7 + 6 = 13 7 + 6 = 13 or 7 + 6 = 13 8. 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 orn =-1 1/2 10. 11. What is the solution? 3n = -24 There is No solution -absolute valueCANNOT be negative. 12. Absolute Value Inequalities x+ 24means the expressionx+ 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 13. Solving Absolute Value Inequalities Solven - 5< 3, graph the solution. n - 5< 3andn - 5> -3+5+5+5+5n < 8andn > 2 2< n < 81 0 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 14. Solving Absolute Value Inequalities Solven - 5> 3, graph the solution. n - 5> 3ORn - 5< -3+5+5+5+5n > 8ORn < 2 1 0 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 15. 16. 17. Attachments