Chapter 6 Solving and Graphing Linear Inequalities 6

Chapter 6 Solving and Graphing Linear Inequalities

6. 1 Solving One-Step Linear Inequalities Objective: -Graph linear inequalities in one variable -Solve one-step linear inequalities

Terms p Graph

Rules p Inequalities n n Use the same rules that you use to solve equations. Starting your Graph p p n Drawing the line p p If you have a > or < use an open circle If you have a > or < use a closed circle Pick a test point. If the test point is true draw your line so that it crosses the test point If your test point is false draw your line away from the test point Special Cases n When you multiply or divide by a negative you have to flip the inequality sign.

Practice p X > -2 p X– 5>1 p -10 < -x p 5 + x > -5

Practice p 15 p < 60 p -a 10 < -2 p -10 a > 100 p 5 + x > -5

White Board Practice p One person from each row get materials for white board practice

6. 2 Solving Multi-Step Linear Inequalities Objective: -Solve multi-step linear inequalities -Use linear inequalities to model and solve real-life problems

Things to Remember n n If you have a > or < use an open circle If you have a > or < use a closed circle When you multiply or divide by a negative you have to flip the inequality sign. Use order of operations in reverse to solve multi-step inequalities

Practice p X + 5 > -13 p 15 – x < 7 p 2(x-8) > -x + 4 p -½x+3<7

6. 3 Solving Compound Inequalities Objective: -Write, solve, and graph compound inequalities -model a real-life problem with a compound inequality

Terms p Compound inequality

Rules Solve each inequality separately p Graph each inequality on the same number line p If it is an AND graph p n p SHADE WHERE THEY CROSS If it is an OR graph n DO NOT SHADE

Practice p 6<x– 6<8 p -4 < 2 + x < 1 p 6 + 2 x > 20 or 8+x<0 p 3 x + 8 > 17 or 2 x + 5 < 7

6. 3 Solving Compound Inequalities Part 2 Objective: -Write, solve, and graph compound inequalities -model a real-life problem with a compound inequality

Missing Assignments p 2 nd hour n Ws 6. 2 p p p n WS 6. 3 p n Brandon Blystone Dalton Mix Breanna Olinger Kyle Reed Cole Robertson Josh Thomas Brandon Blystone Pre-Test p p p Jonathan Crabb Cody Wheat Jeremy Wiggins p 5 th Hour n Ws 6. 1 p n Ws 6. 2 p n AJ Knobelauch Ws 6. 3 p p p n AJ Knobelauch Kristin Burnett AJ Knobelauch Ashlee Lewis Pre-Test p Kristin Burnett

Rules Solve each inequality separately p Graph each inequality on the same number line p If it is an AND graph p n p SHADE WHERE THEY CROSS If it is an OR graph n DO NOT SHADE

Practice problems p 3 n + 3 > 24 or 5 n - 3 < 25 p -43 < 3 x – 10 < -19

Practice problems p 5 x – 10 > 5 or 10 n - 30 < 120 p 15 < 3 x – 9 < 21

6. 4 Solving Absolute Value Equations and Inequalities Objective: -Solve absolute value equations -Solve absolute value inequalities

Terms p Absolute Value p And graph p Or graph

Rules p Get rid of absolute value by making 2 problems p Determine the type of graph (and or or) p Solve both equations p Graph the answers on one number line

Practice p. I x. I=8 p. I x +3 I<8 p. I x– 5 I=7 p. I 3 x + 2 I – 1 > 10

White Board Practice p One person from each row get materials for white board practice

6. 5 Graphing Linear Inequalities in 2 Variables Objective: -Graph linear inequalities in two variables

6. 6 Stem-and-Leaf Plots and Measures of Central Tendency Objective: -Make and use a stem-and-leaf plot -Find the measures of central tendency