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CCSS 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.

Then/Now 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.

Vocabulary open sentence equation solution

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

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

Example 1 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:

Example 1 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: x 2 – 5x

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

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

Example 1b A.x 3 – 2 B.2x 3 C.x 2 – 2 D.2 + x 3 B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number.

Example 1b A.x 3 – 2 B.2x 3 C.x 2 – 2 D.2 + x 3 B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number.

Example 2 Algebraic to Verbal Sentence A. Write a verbal sentence to represent 6 = –5 + x. Answer:

Example 2 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 Algebraic to Verbal Sentence B. Write a verbal sentence to represent 7y – 2 = 19. Answer:

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

Example 2a 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. A. What is a verbal sentence that represents the equation n – 3 = 7?

Example 2a 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. A. What is a verbal sentence that represents the equation n – 3 = 7?

Example 2b 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. B. What is a verbal sentence that represents the equation 5 = 2 + x?

Example 2b 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. B. What is a verbal sentence that represents the equation 5 = 2 + x?

Concept

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

Example 4 Solve One-Step Equations Original equation Simplify.

Example 4 Solve One-Step Equations Answer: Substitute 36 for t. Simplify. CheckOriginal equation ?

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

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

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

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

Example 5 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 + 2Apply the Distributive Property. 53=–3y – 4Simplify the right side. 57=–3yAdd 4 to each side. –19=yDivide each side by –3. Answer:

Example 5 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 + 2Apply the Distributive Property. 53=–3y – 4Simplify the right side. 57=–3yAdd 4 to each side. –19=yDivide each side by –3. Answer: The solution is –19.

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

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

Example 7 ABCDABCD 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.

Example 7 Solve the Test Item Answer: Original equation Subtract 7 from each side. Simplify.

Example 7 Solve the Test Item Answer: C Original equation Subtract 7 from each side. Simplify.

Example 7 A.12 B.6 C.–6 D.–12 If 2x + 6 = –3, what is the value of 2x – 3?

Example 7 A.12 B.6 C.–6 D.–12 If 2x + 6 = –3, what is the value of 2x – 3?