Inequalities Involving Absolute Value

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Presentation transcript:

Inequalities Involving Absolute Value 5-5 Notes for Algebra 1 Inequalities Involving Absolute Value

Cases for solving Absolute values inequalities < Case 1: The expression inside the absolute value symbols is nonnegative Case 2: The expression inside the absolute value symbols is negative

Example 1 pg. 312 Solve Absolute Value Inequalities < Solve each inequality and graph the solution set. 1.) 𝑛−3 < 12 2.) 𝑥+6 <−8

Example 1 pg. 312 Solve Absolute Value Inequalities < Solve each inequality and graph the solution set. 1.) 𝑛−3 < 12 𝑛 −9 < 𝑛 <15 2.) 𝑥+6 <−8 ∅ −15 −9 3 −15 21

Example 2 pg. 313 Apply Absolute Value Inequalities RAINFALL The average annual rainfall in California for the last 100 years is 23 inches. However the annual rainfall can differ by 10 inches from the 100 year average. What is the range of annual rainfall for California?

Example 2 pg. 313 Apply Absolute Value Inequalities RAINFALL The average annual rainfall in California for the last 100 years is 23 inches. However the annual rainfall can differ by 10 inches from the 100 year average. What is the range of annual rainfall for California? 𝑥 13 < 𝑥 < 33

Cases for solving Absolute values inequalities > Case 1: The expression inside the absolute value symbols is nonnegative Case 2: The expression inside the absolute value symbols is negative

Example 3 pg. 313 Solve Absolute Value Inequalities > Solve each inequality then graph the solution set. 1.) 3𝑦−3 >9 2.) 2𝑥+7 > −11

Example 3 pg. 313 Solve Absolute Value Inequalities > Solve each inequality then graph the solution set. 1.) 3𝑦−3 >9 𝑦 𝑦<−2 𝑜𝑟 𝑦>4 −5 −2 1 4 7 2.) 2𝑥+7 > −11 𝑥 𝑥 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 −5 0 5

5-5 pg. 314 9-29o, 30, 31-35o, 48-66(x3)