Warm-Up Solve the linear inequality 1 2 x 4

Warm-Up Solve the linear inequality. 1. 2(x+4) > x + 3 Answers: 1. x > -5 2. x > 1 2. -5 x+7 ≤ 4 x – 2 Homework: WS 1. 7 B Pg. 175 (63 -85 odds)

Homework Answers: HW: Pg. 175 (1 -15 odd, 27 -39 odds)

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. 7 B Solving a Compound Inequality Example 1: Solve and graph the solution set. -3< 2 x +1 ≤ 3 -4 < 2 x ≤ 2 -2 < x ≤ 1 Subtract 1 from each side Divide both sides by 2 Simplify 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: ( -2 ] 0 1

You Try: Solve and graph the solution set. 1 ≤ 2 x + 3 < 11 Answer: [-1, 4) [ -1 ) 4

Solving Inequalities with Absolute Value Rules to follow: If then –c < X c. These rules are valid if < is replaced with ≤ and > is replaced with ≥.

Example 2: Solve and graph the solution set. Given -3 < x-4 <3 Follow rule because of < sign 1

You Try: Solve and graph the solution set. *******Remember to isolate the absolute value sign first. Answer: -5≤x ≤ 5/3, [ -5, 5/3] [ ] -5 0 1 2

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.