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Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM M1 ALGEBRA I Lesson 12: Solving Equations Isolate the variable so that it has a coefficient of 1. Solve an Equation Addition Property of Equality For any numbers a, b, c, if a = b, then a+c=b+c x β 7 = 21 Subtraction Property of Equality For any numbers a, b, c, if a = b, then a-c=b-c x + 7 = 21 Multiplication Property of Equality Division Property of Equality For any numbers a, b, c, if a = b, then ac = bc. For any numbers a, b, c, with c οΉ 0, if a = b, then a=b c c x = 21 7 7x = 21 Solve each equation. a. 6m + 7 = 19 b. 4 β 3x = 5 Lesson 12: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org c. 2x + 7 = 13 3 3 3 d. x β 1 = 5 4 3 12 Solving Equations 5/5/17 S.66 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 66 Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM M1 ALGEBRA I e. Solve for π: 3 2π = 1 f. Solve for π : β4(3s β 1) = 12 β 9π + 5π 4 g. Solve for π¦: 4π¦ β 3 = 5π¦ β 8 Consider the equation 3π₯ + 4 = 8π₯ β 16. Solve for π₯ using the given starting point. Group 1 Subtract 3π₯ from both sides Group 2 Subtract 4 from both sides Lesson 12: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Group 3 Subtract 8π₯ from both sides Group 4 Add 16 to both sides Solving Equations 5/5/17 S.67 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 67 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 M1 ALGEBRA I Consider the equation ππ + π = π β π. a. Verify that this has the solution set {2, β3}. b. Letβs add four to both sides of the equation The new equation is ____________________________________. Verify 2 and -3 are still solutions. c. Letβs now add π₯ to both sides of the equation The new equation is ______________________________________________. Are 2 and -3 still solutions? d. Letβs now subtract π₯ 2 from both sides of the equation The new equation is ______________________________________________. Are 2 and -3 still solutions? Lesson 12: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Solving Equations 5/5/17 S.68 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 68 Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM M1 ALGEBRA I Problem Set 12A Solve the following equations, distribute first to remove parentheses, check your solutions. Show work!!! 1. 2(6π + 8) = 4 + 6π ck. 3. β 16 β 6π£ = β2(8π£ β 7) ck. 5. β 7 β 6π + 5π = 3π β 5π ck. Lesson 12: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org 2. 7 β 8π₯ = 7( 1 + 7π₯) 4. 39 β 8π = β8(3 + 4π) + 3π 6. 7 β 2π₯ = 1 β 5π₯ + 2π₯ ck. ck. ck Solving Equations 5/5/17 S.69 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 69 M1 Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM ALGEBRA I 7. 4(π₯ β 2) = 8(π₯ β 3) β 12 8. β 5(2π β 0.3) + 0.5(4π + 3) = β64 ck. ck. 9. Consider the equation -11 β 2p = 11p + 15. Solve for p using the given starting point. Group 1 Add 2π to both sides Group 2 Subtract 15 from both sides Group 3 Subtract 11p from both sides Group 4 Add 11 to both sides 10. Which of the following equations have the same solution set? Match equations below to each other. Give reasons for your answers that do not depend on solving the equations. I. π₯ β 5 = 3π₯ + 7 II. 3π₯ β 6 = 7π₯ + 8 III. 15π₯ β 9 = 6π₯ + 24 IV. 6π₯ β 16 = 14π₯ + 12 V. 9π₯ + 21 = 3π₯ β 15 VI. β0.05 + Lesson 12: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org π₯ 100 3π₯ = 100 + 0.07 Solving Equations 5/5/17 S.70 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 70