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Properties of Equality and Solving Equations

Learn how to translate verbal expressions into algebraic expressions and equations, solve one-step and multi-step equations, and identify properties of equality.

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Properties of Equality and Solving Equations

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 1–2) CCSS Then/Now New Vocabulary Example 1: Verbal to Algebraic Expression Example 2: Algebraic to Verbal Sentence Key Concept: Properties of Equality Example 3: Identify Properties of Equality Key Concept: Addition and Subtraction / Multiplication and Division Properties of Equality Example 4: Solve One-Step Equations Example 5: Solve a Multi-Step Equation Example 6: Solve for a Variable Example 7: Standardized Test Example Lesson Menu

  3. A. naturals (N), wholes (W), integers (Z) B. wholes (W), integers (Z), reals (R) C. naturals (N), wholes (W), rationals (Q), reals (R) D. naturals (N), wholes (W), integers (Z), rationals (Q), reals (R) 5-Minute Check 1

  4. A. naturals (N), wholes (W) B. reals (R) C. rationals (Q), reals (R) D. integers (Z), reals (R) 5-Minute Check 2

  5. Name the property illustrated by a + (7 + c) = (a + 7) + c. A. Associative Property of Addition B. Distributive Property C. Substitution Property D. Commutative Property of Addition 5-Minute Check 3

  6. Simplify (2c)(3d) + c + 5cd + 3c2. A. 3c2 + 5cd + c B. 3c2 + 11cd + c C. 3c2 + 10cd D. 3c2 + c 5-Minute Check 5

  7. Content Standards A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 8 Look for and express regularity in repeated reasoning. CCSS

  8. You used properties of real numbers to evaluate expressions. • Translate verbal expressions into algebraic expressions and equations, and vice versa. • Solve equations using the properties of equality. Then/Now

  9. open sentence • equation • solution Vocabulary

  10. Verbal to Algebraic Expression A. Write an algebraic expression to represent the verbal expression 7 less than a number. Answer:n – 7 Example 1

  11. Verbal to Algebraic Expression B. Write an algebraic expression to represent the verbal expression the square of a number decreased by the product of 5 and the number. Answer:x2 – 5x Example 1

  12. A. Write an algebraic expression to represent the verbal expression 6 more than a number. A. 6x B.x + 6 C.x6 D.x – 6 Example 1a

  13. B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number. A.x3 – 2 B. 2x3 C.x2 – 2 D. 2 + x3 Example 1b

  14. Algebraic to Verbal Sentence A. Write a verbal sentence to represent 6 = –5 + x. Answer: Six is equal to –5 plus a number. Example 2

  15. Algebraic to Verbal Sentence B. Write a verbal sentence to represent 7y – 2 = 19. Answer: Seven times a number minus 2 is 19. Example 2

  16. A. What is a verbal sentence that represents the equation n – 3 = 7? A. The difference of a number and 3 is 7. B. The sum of a number and 3 is 7. C. The difference of 3 and a number is 7. D. The difference of a number and 7 is 3. Example 2a

  17. B. What is a verbal sentence that represents the equation 5 = 2 + x? A. Five is equal to the difference of 2 and a number. B. Five is equal to twice a number. C. Five is equal to the quotient of 2 and a number. D. Five is equal to the sum of 2 and a number. Example 2b

  18. Concept

  19. Identify Properties of Equality A. Name the property illustrated by the statement. a – 2.03 = a – 2.03 Answer: Reflexive Property of Equality Example 3

  20. Identify Properties of Equality B. Name the property illustrated by the statement. If 9 = x, then x = 9. Answer: Symmetric Property of Equality Example 3

  21. A. What property is illustrated by the statement? If x + 4 = 3, then 3 = x + 4. A. Reflexive Property of Equality B. Symmetric Property of Equality C. Transitive Property of Equality D. Substitution Property of Equality Example 3a

  22. B. What property is illustrated by the statement? If 3 = x and x = y, then 3 = y. A. Reflexive Property of Equality B. Symmetric Property of Equality C. Transitive Property of Equality D. Substitution Property of Equality Example 3b

  23. Concept

  24. ? 5.5 – 5.48 = 0.02 Substitute 5.5 for m. Solve One-Step Equations A.Solve m – 5.48 = 0.02. Check your solution. m – 5.48 = 0.02 Original equation m – 5.48 + 5.48 = 0.02 + 5.48 Add 5.48 to each side. m = 5.5 Simplify. Check m – 5.48 = 0.02 Original equation 0.02 = 0.02 Simplify.  Answer: The solution is 5.5. Example 4

  25. Solve One-Step Equations Original equation Simplify. Example 4

  26. Check Original equation ? Solve One-Step Equations Substitute 36 for t. Simplify.  Answer: The solution is 36. Example 4

  27. A. What is the solution to the equation x + 5 = 3? A. –8 B. –2 C. 2 D. 8 Example 4a

  28. B. What is the solution to the equation A.5 B. C.15 D.30 Example 4b

  29. Solve a Multi-Step Equation Solve 53 = 3(y – 2) – 2(3y – 1). 53 = 3(y – 2) – 2(3y – 1) Original equation 53 = 3y – 6 – 6y + 2 Apply the Distributive Property. 53 = –3y – 4 Simplify the right side. 57 = –3y Add 4 to each side. –19 = y Divide each side by –3. Answer: The solution is –19. Example 5

  30. A.–6 B. C. D.6 What is the solution to 25 = 3(2x + 2) – 5(2x + 1)? Example 5

  31. End of the Lesson

  32. Pages 22 – 23 #22 – 27, 36 – 42, 45 – 50

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