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Warm-Up Solve the linear inequality. 1. 2(x+4) > x + 3 Answers: 1. x > -5 2. x > 1 2. -5x+7 ≤ 4x – 2 Homework: WS 1.7B Pg. 175 (63-85 odds) Homework Answers: HW: Pg. 175 (1-15 odd, 27-39odds) Announcements: Ch #1 TEST – 100 point on 9/15 & 18! YOU must buy your $20 text book by Sept 11!!!!!!!! THANK YOU Objective: To be able to use interval notation when solving linear inequalities, recognize inequalities with no solution or all real numbers as a solution, solve compound inequalities and solve absolute value inequalities. Lesson 1.7B Solving a Compound Inequality The solution consists all real numbers greater Example 1: set Solve and of graph the solution set. than -2 less 1, represented by side -3<and 2x +1 ≤ 3than or equal toSubtract 1 from each { x< -2< notation andsides (-2,1] -4 2x ≤x2≤ 1} in set-builder Divide both byin2 interval notation. ( ] -2 < x ≤ 1 Simplify The graph is: ( -2 ] 0 1 You Try: Solve and graph the solution set. 1 ≤ 2x + 3 < 11 Answer: [-1, 4) [ -1 ) 4 Solving Inequalities with Absolute Value Rules to follow: If X c then –c < X <c. If X c then X < -c or X > c. These rules are valid if < is replaced with ≤ and > is replaced with ≥. Example 2: Solve and graph the solution set. x 4 3 Given -3 < x-4 <3 Follow rule because of < sign 1<x<7 Add four to both sides The solution set is (1,7). ( ) 1 7 You Try: Solve and graph the solution set. *******Remember to isolate the absolute value sign first. 2 3x 5 7 13 Answer: -5≤x ≤ 5/3, [ -5, 5/3] [ ] -5 0 1 2 Example 3: 7 5 2 x Given Switch equation around 5 2 x 7 Rewrite following rule 5 2 x7or 5 2 x 7 Solve 2 x12or 2 x 2 Remember when dividing x 6 or x 1 by a negative to switch the signs 1 ) 6 ( The solution set is (-∞, -1) OR (6,∞) You Try!! 18 6 3x Answer: (-∞, -4) OR (8, ∞) Graph ) -4 ( 8 Summary: Describe how to solve an absolute value equation involving the > symbol.