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Lesson #17 Warm UP 1. Which number is a solution of the inequality? 4m> 8 a. 3 b. -2 c. 2 d. ½ 2. Write an inequality for the graph. -3/4 3. Jamie can run at least 10 mph. Write and graph an inequality to model this situation. Algebra I Notes #17 Title: Compound Inequalities Objective: To solve and graph compound inequalities. Vocabulary • Compound Inequality – two inequalities joined with “and” or “or” “and” means – intersection, conjunction “or” U means – union, disjunction U Example “and” Example “or” Example 1) Graph and write an inequality All real number greater than or equal to 0 and less than 4. “and” Statement- Conjunctions These statement must contain both solutions x > a and x < b. a < x < b x is between (a) and (b) x is less than (b) and greater than (a) a ≤ x ≤ b x is between (a) and (b) inclusive Example 2 Goal is to get “X” by itself in the middle. Must do the same thing to all sides • -2 ≤ 3x – 8 ≤ 10 Example 3 • -12 < 2x -6 < 4 Example 4 Solve each side then put together 2x < 8 and 3x + 2 > -4 “or” Statement -Disjunction An inequality that can belong to one another or both inequalities. A union of two inequalities. x < a or x > b (x) is less than a union with (x) greater than (b) Example 1 • Write and graph an inequality for all real number that are less than -1 or greater than 2. Example 2 • 3x – 1 < 2 or 2x + 2 ≥ 8 Example 3 • 3x + 2 < -1 or 4- x ≤ 2