Warm-Up Solve the linear inequality. 1. 2(x+4) > x x+7 ≤ 4x – 2 Homework: WS 1.7B Pg. 175 (63-85 odds) Answers: 1. x > x > 1

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 set consists of all real numbers greater than -2 and less than or equal to 1, represented by { x -2< x ≤ 1} in set-builder notation and (-2,1] in interval notation. ( ] The graph is: ( ] Example 1: Solve and graph the solution set. -3< 2x +1 ≤ 3Subtract 1 from each side -4 < 2x ≤ 2Divide both sides by 2 -2 < x ≤ 1Simplify

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 then –c < X <c. If then X c. These rules are valid if is replaced with ≥.

Example 2: Solve and graph the solution set. 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. Answer: -5≤x ≤ 5/3, [ -5, 5/3] [ ]

Example 3: Given Switch equation around Rewrite following rule Solve Remember when dividing by a negative to switch the signs The solution set is (-∞, -1) OR (6,∞) ) (

You Try!! Answer: (-∞, -4) OR (8, ∞) Graph ) ( -4 8 Summary: Describe how to solve an absolute value equation involving the > symbol.