algebra-i-m1-topic-c-lesson-11-teacher (4).pdf - Lesson 11 NYS COMMON CORE MATHEMATICS CURRICULUM M1 ALGEBRA I Lesson 11 Solution Sets for Equations and

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NYS COMMON CORE MATHEMATICS CURRICULUM M1 Lesson 11 ALGEBRA I Lesson 11: Solution Sets for Equations and Inequalities 145 This work is derived from Eureka Math and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M1-TE-1.3.0-07.2015 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 11: Solution Sets for Equations and Inequalities Student Outcomes Students understand that an equation with variables is often viewed as a question asking for the set of values one can assign to the variables of the equation to make the equation a true statement. They see the equation as a “filter” that sifts through al l numbers in the domain of the variables, sorting those numbers into two disjoint sets: the solution set and the set of numbers for which the equation is false. Students understand the commutative, associate, and distributive properties as identities (i.e., equations whose solution sets are the set of all values in the domain of the variables). Classwork Example 1 (2 minutes) Consider the equation shown in Example 1 of your student materials, ? 2 = 3? + 4 , where ? represents a real number. Since we have not stated the value of ? , this is not a number sentence. Example 1 Consider the equation, ? ? = ?? + ? , where ? represents a real number. a. Are the expressions ? ? and ?? + ? algebraically equivalent? No. Then, we cannot guarantee there will be any real value of ? that will make the equation true. b. The following table shows how we might “sift” through various values to assign to the variable symbol ? in the hunt for values that would make the equation true. ? -VALUE THE EQUATION TRUTH VALUE Let ? = ? ? ? = ?(?) + ? FALSE Let ? = ? ? ? = ?(?) + ? FALSE Let ? = ? ? ? = ?(?) + ? FALSE Let ? = −? (−?) ? = ?(−?) + ? FALSE Let ? = ? ? ? = ?(?) + ? TRUE Let ? = ? ? ? = ?(?) + ? FALSE Let ? = ?? ?? ? = ?(??) + ? FALSE Let ? = −? (−?) ? = ?(−?) + ? FALSE
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NYS COMMON CORE MATHEMATICS CURRICULUM M1 Lesson 11 ALGEBRA I Lesson 11: Solution Sets for Equations and Inequalities 146 This work is derived from Eureka Math and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M1-TE-1.3.0-07.2015 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Of course, we should sift through ALL the real numbers if we are seeking all values that make the equation ? 2 = 3? + 4 true. (This makes for quite a large table!) So far, we have found that setting ? equal to 4 yields a true statement. Look at the image in your student materials. Can you see what is happening here and how it relates to what we have been discussing? The numbers are going down the road and being accepted into the solution set or rejected based on whether or not the equation is true. There happens to be just one more value we can assign to x that makes ? 2 = 3? + 4 a true statement. Would you like to continue the search to find it?
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