1. Splash Screen

2. Mathematical Practices
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

3. 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

4. open sentence
equation
solution
Vocabulary

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

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

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:
Example 1

8. 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

9. 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

10. 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

11. 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

12. 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

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

14. A. Write a verbal sentence to represent 6 = –5 + x.
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. B. Write a verbal sentence to represent 7y – 2 = 19.
Algebraic to Verbal Sentence
B. Write a verbal sentence to represent 7y – 2 = 19.
Answer:
Example 2

16. B. Write a verbal sentence to represent 7y – 2 = 19.
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

17. 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

18. 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

19. 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

20. 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

21. Concept

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

23. A. Name the property illustrated by the statement. a – 2.03 = a – 2.03
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

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

25. Answer: Symmetric 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
Example 3

26. A. Reflexive Property of Equality B. 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
B. Symmetric Property of Equality
C. Transitive Property of Equality
D. Substitution Property of Equality
Example 3a

27. A. Reflexive Property of Equality B. 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
B. Symmetric Property of Equality
C. Transitive Property of Equality
D. Substitution Property of Equality
Example 3a

28. A. Reflexive Property of Equality 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
B. Symmetric Property of Equality
C. Transitive Property of Equality
D. Substitution Property of Equality
Example 3b

29. A. Reflexive Property of Equality 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
B. Symmetric Property of Equality
C. Transitive Property of Equality
D. Substitution Property of Equality
Example 3b

30. Concept

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

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

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

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

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

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

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

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

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

40. 53 = 3(y – 2) – 2(3y – 1) Original equation
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:
Example 5

41. 53 = 3(y – 2) – 2(3y – 1) Original equation
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

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

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

44. Subtract πr 2 from each side.
Solve for a Variable
Surface area formula
Subtract πr 2 from each side.
Simplify.
Example 6

45. Solve for a Variable
Divide each side by πr.
Simplify.
Example 6

46. Solve for a Variable
Divide each side by πr.
Simplify.
Example 6

47. 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. D.
Example 6a

48. 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. D.
Example 6a

49. 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.
Example 7

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

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

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

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

54. End of the Lesson