1. Equations and Inequalities
Chapter 4
Equations and
Inequalities

2. Evaluating and Writing Algebraic Expressions
Lesson 4-1
Evaluating and Writing Algebraic Expressions

3. Vocabulary Variable – a symbol that represents one or more numbers
Algebraic expression – a mathematical phrase (number sentence) with at least one variable
***You must THINK your way through this!!

4. Writing word Phrases Words: $4 per poster times the number of posters
Expression: · p
Written Algebraically: 4p
Words: six goals fewer than g goals
Expression:
Written Algebraically:

5. Phrases that mean “ADD”
More than
Added to
Sum
Plus
Increased by
Others? 

6. Phrases that mean “Subtract”
Difference of
Minus
Subtracted from
Less than
Decreased by
Less
Others?

7. Phrases that mean “Multiply”Of
Groups of
Product
Times
Multiply
Twice
Others? 

8. Phrases that mean “Divide”
Quotient
Divide
Ratio
Into
Others? 

9. Write an algebraic expression for the quantity “three more than half a number”.
2. Write an algebraic expression for the quantity “one-fifth of a number reduced by double the same number”.

10. 3. The number of boxes of cookies sold by Sarah was 43 fewer than the number of boxes of cookies sold by Keiko. The number of boxes of cookies sold by Imelda was 53 more than the number sold by Keiko. Write algebraic expressions for these relations.
4. The first angle of a triangle is 16 degrees less than the second angle. The angle is double the second angle. Write
algebraic expressions for these relations.

11. 5. Kentucky has about half the land area of Minnesota
5. Kentucky has about half the land area of Minnesota. The land area of Maine is approximately two-fifths the land area
of Minnesota. Write algebraic expressions for these relations.
6. A census of a middle school found that the number of 7th graders was fifty more than the number of eighth graders. The number of sixth graders was three-fourths the number of eighth graders. Write algebraic expressions for these relations.

12. 7. In an archery tournament, the number of points awarded for an arrow in the gold circle (bull’s eye) is six less than
triple the points awarded for an arrow in the blue ring. Write algebraic expressions for these relations.

13. Evaluating Algebraic Expressions
Evaluate for p = 2, n = 3, and s = 5 2p + 7 p + (n · s) 2(2) + 7 Substitute (plug it in) 2 + (3)(5) Solve using PEMDAS 17 11

14. Assignment Textbook p. 171 # 12-24/e, 25-30 all, 32-36/e, 40-44
Lesson for Tuesday and Wednesday 1/4 & 1/5

15. Using Number Sense to Solve Equations
Lesson 4-2
Using Number Sense to Solve Equations

16. Vocabulary Equation – a number sentence with an equal sign
Solution of an equation – the value for a variable that makes the equation true
Remember – equal means the same on both sides; balanced

17. Solve using Substitution
n – 27 = 38; 11, 51, or 65

18. Solve using Mental Math

19. Assignment
P. 176 # 10-22/e, 23-25, 33, 38-42
{p. 176 # 10, 14, 18, 22, 23, 25, 33, 38, 39, 40, 41, 42}
Work for Thursday 1/6 (still due on Friday)

20. Solving Equations by Adding or Subtracting
Lesson 4-3
Solving Equations by Adding or Subtracting

21. Vocabulary
Inverse operations – operations that undo each other to get the variable alone

22. Key Concept Addition Property of Equality
If you add the same value to each side of an equation, the two sides remain equal:
20/2=10 so 20/2 + 3 =
Subtraction Property of Equality
If you subtract the same value to each side of an equation, the two sides remain equal:
12/2=6 so 12/2 -4 = 6 - 4

23. Examples

24. Assignment Lesson 4-3 P. 183 # 5-29/all, 40-44/all
{p. 183 # 6-28/e, 40-44/all}
Tuesday (Due Friday, No time to make up, it’s on this six week’s grade)

25. Solving Equations by Multiplying or Dividing
Lesson 4-4
Solving Equations by Multiplying or Dividing

26. Key Concept
Since multiplication and division are inverse operations, multiplication undoes division and division undoes multiplication.
Example:
(4 ∙ 9) ÷ 4 = 9
3/5 ∙ 5 = 3

27. Examples

28. Assignment Lesson 4-4 P. 189 # 9-36/all, 53-57/all
{p. 189 # 10-36/e, 53-57/all}
Wednesday

29. Exploring Two-Step Problems
Lesson 4-5
Exploring Two-Step Problems

30. Vocabulary
A(n) _____________ is a mathematical phrase (number sentence) with at least one variable.
Algebraic Expression

31. Examples
Define a variable and write an algebraic expression for the phrase “$10 plus $5 times the number of roses ordered”
Define the variable: Let ___= unknown
(# roses ordered)
Write an algebraic expression:

32. Examples
Define a variable and write an algebraic expression for “a man is two years younger than three times his son’s age”
Define the variable: Let ___= unknown
( )
Write an algebraic expression:

34. Assignment Lesson 4-5
P. 197 # 8-12/all, 14-26/e, 27-28, 38-40/all, 43-48/all
{p. 197 # 8, 10, 12, 14, 18, 22, 26, 27, 38, 40, 43-48}
Tuesday

35. Solving Two-Step Problems
Lesson 4-6
Solving Two-Step Problems

36. Examples

37. Assignment Lesson 4-6 P. 203 # 6-34/e, 43-48
Wednesday

38. Graphing Inequalities
Lesson 4-7
Graphing Inequalities

39. Examples

40. Assignment Lesson 4-7 P. 207 # 8-28/e, 37-41
Thursday (Due Friday )

41. Solving Inequalities with Addition and Subtraction
Lesson 4-8
Solving Inequalities with Addition and Subtraction

42. Examples

43. Assignment Lesson 4-8 P. 212 # 8-32/e, 40-46
Monday (Due Friday )

44. Solving Inequalities by Multiplying and Dividing
Lesson 4-9
Solving Inequalities by Multiplying and Dividing

45. Examples

46. Assignment Lesson 4-8 TEST WEDNESDAY 2-2-11 P. 217 # 6-38/e, 50-53
Monday
(Due Wednesday )
TEST WEDNESDAY