Lesson 3-6: Compound Inequalities W - Math Men
Lesson 3-6: Compound InequalitiesName:hen people plan a house, they often have many requirements in mind that can bewritten as inequalities. Such requirements could be the dimensions of rooms or theoverall size of the house. In this activity, we will investigate what happens when wecombine requirements. First, we will graph each requirement separately, then we will graphcombinations of those requirements. Here are the basic requirements we will work with:WDimension Requirements:Requirement A: d 5 ftRequirement B: d 12 ftRequirement C: d 10 ftArea Requirements:Requirement D: A 1500 sq ftRequirement E: A 1200 sq ftRequirement F: A 1800 sq ft1. First, let’s investigate what happens when we combine requirements A & B with “and”:a. Graph the numbers that meet requirement A:b. Graph the numbers that meet requirement B:468101214468101214468101214c. Graph only the numbers that meet both A and B:d. Write the solution as an inequality:2. Now let’s investigate what happens when we combine requirements A & B with “or”:a. Graph the numbers that meet requirement A:b. Graph the numbers that meet requirement B:c. Graph all the numbers that meet either A or B:d. Write the solution as an inequality:4681012144681012144681012143. Now investigate what happens when we combine requirements A & C with “and”:a. Graph the numbers that meet requirement A:b. Graph the numbers that meet requirement C:c. Graph only the numbers that meet both A and C:468101214468101214468101214d. Write the solution as an inequality:4. Investigate what happens when we combine requirements A & C with “or”:a. Graph the numbers that meet requirement A:b. Graph the numbers that meet requirement C:c. Graph all the numbers that meet either A or C:d. Write the solution as an inequality:Mastery Algebra 1OBJ: Graphing compound inequalities4681012144681012144681012143-6.A
Each graph that you have drawn on a number line represents the solution set or truth set.Solution Set (or Truth Set)A solution set is all the numbers that make a statement true.5. Next, combine requirements D & E:a. Graph the numbers that meet requirement D:b. Graph the numbers that meet requirement E:c. Graph the numbers that meet requirements D and E:d. Graph all the numbers that meet requirement D or 130016001900100013001600190010001300160019006. Now combine requirements E & F:a. Graph the numbers that meet requirement E:b. Graph the numbers that meet requirement F:c. Graph the numbers that meet requirements E and F:d. Graph all the numbers that meet requirement E or F:7. Now combine requirements D & F:a. Graph the numbers that meet requirement D:b. Graph the numbers that meet requirement F:c. Graph the numbers that meet requirements D and F:d. Graph all the numbers that meet requirement D or F:8. Now combine requirements B & C:a. Graph the numbers that meet requirement B:b. Graph the numbers that meet requirement C:c. Graph the numbers that meet requirements B and C:468101214468101214468101214468101214d. Graph all the numbers that meet requirement B or C:9. Now write some notes to help you remember what you have learned about combiningsolution sets using the words and & or.Mastery Algebra 1OBJ: Graphing compound inequalities3-6.B
More 3-6: Lines DancingGraphing Compound InequalitiesCombining two inequalities with the word “or” creates the union of the two solution sets.The symbol for the union of two sets is “ ”. Any value that is in the solution set to either of theoriginal inequalities is in the solution set of compound inequality.Combining two inequalities with the word “and” creates the intersection of the two solution sets.The symbol for the intersection of two sets is “ ”. Only values that are in the solution set to bothoriginal inequalities may be in the solution set of the compound inequality.Use the table of inequality requirements below to find each union or intersection. Sketch eachindividual requirement first, and then sketch the compound inequality on the third number line.Requirement A:x 3Requirement B:x 2Requirement C:x 0Requirement D:x 1Requirement E:x 4Requirement F:x 2Requirement G:x 01. Requirements A and 5-3-1135C:A C:Solution:2. Requirements A or C.A:C:A C:Solution:3.Requirements B and D.4.B:Requirements B or 135-5-3-1135B D:B D:Solution:Solution:5.6.Requirements A and B.A:Requirements A or 5B:A B:A B:-5Solution:Mastery Algebra 1-3-1135Solution:OBJ: Graphing compound inequalities3-6.C
Graph each set of requirements as indicated and write the solution as an inequality. Rememberto label each number line!7.Requirements E and G.8.Requirements E or 3-1135Solution:Solution:9.10.Requirements C and D.Requirements C or 3-1135Solution:Solution:11.12.Requirements B and C.Requirements D or 3-1135Solution:Solution:13.14.Requirements A and 3-1135Solution:15.Requirements B or F.Solution:Based on these graphs, what generalizations can you make about the differences betweenthese two types of compound inequalities (unions and intersections)?Mastery Algebra 1OBJ: Graphing compound inequalities3-6.D
Even More 3-6: Compounding InequitiesSolve each compound inequality. Graph the solutions on the number line AND state 3 numbersin the solution set. Show all your work!1. 4m 5 7 or 4m 5 9-5Solution:053 numbers in the solution set:2. 1 x 2 4-5Solution:053 numbers in the solution set:3. y 6 1 or y 2 4-5Solution:053 numbers in the solution set:4. 2(5 x) 12 and 7 x 4 x 9-5Solution:053 numbers in the solution set:5. 6 2 x 2 0-5Solution:053 numbers in the solution set:6. 3 y 11 14 or 2 y 5 y 12-5Solution:053 numbers in the solution set:Algebra 1OBJ: Practice solving and graphing compound inequalities3-6.E
7. 3(c 4) 12 and c 2 5-505Solution:3 numbers in the solution set:8. 3 2k 7 or 2k 13 1-505Solution:3 numbers in the solution set:9. 2(3w 5) 7 or 2w 8 5w 1-505Solution:3 numbers in the solution set:10. 8 2( x 3) 4 14-505Solution:3 numbers in the solution set:Algebra 1OBJ: Practice solving and graphing compound inequalities3-6.F
Practice 3-6Name:Date: Period:Solve each compound inequality and graph the solution:1. 5 x 5 52.k 3 1 or k 3 13. 4d 8 and 2d 64. 6 9 3y 65.4 2 x 7 and 2 3( x 1) 56.8(3 x 6) 24 or 2(3b 2) 4b 87.6 2(4 x 1) 10 and 5 ( x 9) 2 x 7Algebra 1Obj: practice solving compound inequalitiesPractice 3-6
Algebra 1 OBJ: Practice solving and graphing compound inequalities 3-6.E S olve each compound inequality. Graph the solutions on the number line AND state 3 numbers in the solution set. Show all your work! 1. 4m 5! 7 or 4m 5 9-Solution: 3 numbers in the solution set: 2. d d1 2 4x Solution: 3 numbers in the solution set: 3. y 6! 1 or y 2d4-
Inequalities Write simple and compound inequalities. Graph compound inequalities. Solve compound inequalities. A.CED.1 A.CED.2 A.REI.3!Compound inequality!Solution of a compound inequality!Conjunction!Disjunction! This chapter reviews solving linear equations and inequalities with an emphasis towards connecting the numeric, graphic .
Solving & Graphing Inequalities 2016-01-11 www.njctl.org Slide 3 / 182 Table of Contents Simple Inequalities Addition/Subtraction Simple Inequalities Multiplication/Division Solving Compound Inequalities Special Cases of Compound Inequalities Graphing Linear Inequalities in Slope-Intercept Form click on the topic to go to that section Glossary .
2 Solving Linear Inequalities SEE the Big Idea 2.1 Writing and Graphing Inequalities 2.2 Solving Inequalities Using Addition or Subtraction 2.3 Solving Inequalities Using Multiplication or Division 2.4 Solving Multi-Step Inequalities 2.5 Solving Compound Inequalities Withdraw Money (p.71) Mountain Plant Life (p.77) Microwave Electricity (p.56) Digital Camera (p.
Compound inequalities are two inequalities joined by the word and or by the word or. Inequalities joined by the word and are called conjunctions. Inequalities joined by the word or are disjunctions. You can represent compound inequalities using words, symbols or graphs. 20. Complete the table. Th e fi rst two rows have been done for you. Verbal .
Compound Inequalities The inequalities you have seen so far are simple inequalities. When two simple inequalities are combined into one statement by the words AND or OR, the result is called a compound inequality. NOTE the following symbols: Λ means AND V means OR
4 Step Phonics Quiz Scores Step 1 Step 2 Step 3 Step 4 Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 . Zoo zoo Zoo zoo Yoyo yoyo Yoyo yoyo You you You you
Chapter 4D-Quadratic Inequalities and Systems Textbook Title Learning Objectives # of Days 4.9 Graph Quadratic Inequalities 12. Graph quadratic inequalities and systems of quadratic inequalities on the coordinate plane. (4.9) 2 4.9 Systems of Inequalities 13. Graph systems of inequalities involving linear, quadratic and absolute value functions .
Pre-AP Algebra 2 Lesson 2-5 –Graphing linear inequalities & systems of inequalities Objectives: The students will be able to - graph linear functions in slope-intercept and standard form, as well as vertical and horizontal lines. - graph linear & non-linear inequalities and systems of inequalities, and describe the shaded region as the set
