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Five-Minute Check (over Lesson 1–2) 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 Over Lesson 1–2 A. naturals (N), wholes (W), integers (Z) 0% B 0% A D. naturals (N), wholes (W), integers (Z), rationals (Q), reals (R) A B C 0% D D C. naturals (N), wholes (W), rationals (Q), reals (R) A. B. C. 0% D. C B. wholes (W), integers (Z), reals (R) Over Lesson 1–2 A. naturals (N), wholes (W) B. reals (R) 0% B A 0% A B C 0% D D D. integers (Z), reals (R) A. B. C. 0% D. C C. rationals (Q), reals (R) Over Lesson 1–2 Name the property illustrated by a + (7 + c) = (a + 7) + c. A. Associative Property of Addition 0% B 0% A D. Commutative Property of Addition A B C 0% D D C. Substitution Property A. B. C. 0% D. C B. Distributive Property Over Lesson 1–2 Name the property illustrated by 3(4 + 0.2) = 3(4) + 3(.02). A. Associative Property of Addition 0% B A D. Substitution Property 0% A B C 0% D D C. Distributive Property A. B. C. 0% D. C B. Identity Property Over Lesson 1–2 Simplify (2c)(3d) + c + 5cd + 3c2. A. 3c2 + 5cd + c B. 3c2 + 11cd + c A B C 0% D D 0% B 0% A D. 3c2 + c C C. 3c2 + 10cd A. B. C. 0% D. Over Lesson 1–2 Which equation illustrates the Additive Identity Property? A. 5 + 0 = 5 0% B A D. 0% A B C 0% D D C. 5 + (–5) = 0 A. B. C. 0% D. C B. 5(1) = 5 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. • open sentence • equation • solution Verbal to Algebraic Expression A. Write an algebraic expression to represent the verbal expression 7 less than a number. Answer: n – 7 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 A. Write an algebraic expression to represent the verbal expression 6 more than a number. A. 6x B. x + 6 A B C 0% D D 0% B 0% A D. x – 6 C C. x6 A. B. C. 0% D. B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number. A. x3 – 2 B. 2x3 A B C 0% D D 0% B 0% A D. 2 + x3 C C. x2 – 2 A. B. C. 0% D. Algebraic to Verbal Sentence A. Write a verbal sentence to represent 6 = –5 + x. Answer: Six is equal to –5 plus a number. Algebraic to Verbal Sentence B. Write a verbal sentence to represent 7y – 2 = 19. Answer: Seven times a number minus 2 is 19. A. What is a verbal sentence that represents the equation n – 3 = 7? A. The difference of a number and 3 is 7. 0% B 0% A D. The difference of a number and 7 is 3. A B C 0% D D C. The difference of 3 and a number is 7. A. B. C. 0% D. C B. The sum of a number and 3 is 7. 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. 0% B 0% A D. Five is equal to the sum of 2 and a number. A B C 0% D D C. Five is equal to the quotient of 2 and a number. A. B. C. 0% D. C B. Five is equal to twice a number. Identify Properties of Equality A. Name the property illustrated by the statement. a – 2.03 = a – 2.03. Answer: Reflexive Property of Equality Identify Properties of Equality B. Name the property illustrated by the statement. If 9 = x, then x = 9. Answer: Symmetric Property of Equality A. What property is illustrated by the statement? If x + 4 = 3, then 3 = x + 4. A. Reflexive Property of Equality 0% B 0% A D. Substitution Property of Equality A B C 0% D D C. Transitive Property of Equality A. B. C. 0% D. C B. Symmetric Property of Equality B. What property is illustrated by the statement? If 3 = x and x = y, then 3 = y. A. Reflexive Property of Equality 0% B 0% A D. Substitution Property of Equality A B C 0% D D C. Transitive Property of Equality A. B. C. 0% D. C B. Symmetric Property of Equality 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 Check m – 5.48 = 0.02 ? 5.5 – 5.48 = 0.02 0.02 = 0.02 Answer: The solution is 5.5. Simplify. Original equation Substitute 5.5 for m. Simplify. Solve One-Step Equations Original equation Simplify. Solve One-Step Equations Check Original equation ? Substitute 36 for t. Simplify. Answer: The solution is 36. A. What is the solution to the equation x + 5 = 3? A. –8 B. –2 0% B A 0% A B C 0% D D D. 8 C C. 2 A. B. C. 0% D. B. What is the solution to the equation A. 5 B. 0% B A 0% A B C 0% D D D. 30 C C. 15 A. B. C. 0% D. 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. What is the solution to 25 = 3(2x + 2) – 5(2x + 1)? A. –6 B. 0% B A 0% A B C 0% D D D. 6 C C. A. B. C. 0% D. Solve for a Variable Area formula Subtract πr 2 from each side. Simplify. Solve for a Variable Divide each side by πr. Simplify. GEOMETRY The formula for the perimeter of a rectangle is where P is the perimeter, and w is the width of the rectangle. What is this formula solved for w? A. B. C. 0% D 0% C 0% B A D. 0% A. B. C. D. A B C D A B C D Read the Test Item You are asked to find the value of the expression 4g – 2. Your first thought might be to find the value of g and then evaluate the expression using this value. Notice that you are not required to find the value of g. Instead, you can use the Subtraction Property of Equality. Solve the Test Item Original equation Subtract 7 from each side. Simplify. Answer: C If 2x + 6 = –3, what is the value of 2x – 3? A. 12 B. 6 0% B A 0% A B C 0% D D D. –12 C C. –6 A. B. C. 0% D.