This document provides instructions and examples for solving addition, subtraction, multiplication, and division equations. It defines key terms like variables, algebraic expressions, and evaluating expressions. Examples are given for writing algebraic expressions to represent word phrases. The document also shows how to simplify expressions and evaluate expressions for a given value of a variable.

2. ADDITION & SUBTRACTION
EQUATIONS
1. SOLVE FOR X
3. WHAT EVER YOU DO TO
ONE SIDE YOU HAVE TO DO
TO THE OTHER
2. ADD THE OPPOSITE TO
BOTH SIDES

3. Problem 1
X + 4 = 23
X = 23 - 4
X = 18

4. Problem 2
X - 11 = 31
X = 31 + 11
X = 42

5. Problem 3
X + 3 = -35
X = -35 - 3
X = -38

6. Problem 4
X - 21 = -22
X = -22 + 21
X = -1

7. Problem 5
X + 8 = 20
X = 20 - 8
X = 12

8. Problem 6
X - 4 = 12
X = 12 + 4
X = 16

9. Problem 7
X + 9 = 22

10. Problem 8
X + 1 = 28

11. Problem 9
X - 13 = 45

12. Problem 10
X + 13 = 45

13. Problem 11
-2 + X = -11
X = -11 + 2
X = -9

14. Problem 12
X - 6 = -25

15. Problem 13
19 + X = -20
X = -20 - 19
X = -39

16. Problem 14
22 = X + 3

17. Problem 15
20 = X + 30

18. Problem 16
30 = X - 30

19. Problem 17
X + 14 = 7

20. Problem 18
-22 = 7 + X

21. Problem 19
X + 15 = 85

22. Problem 20
-23 = -21 + X

23. MULTIPLICATION
EQUATIONS
1. SOLVE FOR X
3. WHAT EVER YOU DO TO
ONE SIDE YOU HAVE TO DO
TO THE OTHER
2. DIVIDE BY THE NUMBER
IN FRONT OF THE VARIABLE

24. Problem 1
4X = 16

25. Problem 2
2X = -14

26. Problem 3
17X = 34

27. Problem 4
-9X = 36

28. Problem 5
8X = -16

29. Problem 6
-9X = -27

30. Problem 7
-14X = 0

31. Problem 8
-X = -99

32. Problem 9
10X = 5

33. Problem 12
9X = 3

34. Problem 17
10X = 0

35. Problem 10
9 = 3X

36. Dividing using Algebra
Do each separate division problem

37. Problem 11
X = 5
2

38. Problem 13
X = 6
3

39. Problem 14
X = -2
6

40. Problem 15
X = 2
3

41. Problem 16
X = 3
15

42. Problem 18
X = -4
9

43. Problem 19
X = -5
-4

44. Problem 20
X = -6
3

45. Problem 1
c
3
= 4

46. Problem 2
x
8
= 3

47. Problem 3
b
4
= 6

48. Problem 4
2a
3
= 6

49. Problem 5
3r
5
= 3

50. Problem 6
9n
3
= 12

51. Problem 7
8m
2
= 12

52. Algebra I
By Miss Pampel

53. Definitions
•Variable – A variable is a letter
or symbol that represents a
number (unknown quantity).
•8 + n = 12

54. Definitions
•A variable can use any letter of
the alphabet.
•A number plus 5 n + 5
•A number less than 7 x – 7
•A number minus 25 w - 25

55. Definitions
•Algebraic expression – a group of
numbers, symbols, and variables
that express an operation or a
series of operations.
• m + 8
• r – 3

56. Definitions
•Evaluate an algebraic expression –
To find the value of an algebraic
expression by substituting numbers
for variables.
• m + 8 m = 2 2 + 8 = 10
• r – 3 r = 5 5 – 3 = 2

57. Words That Lead to Addition
•Sum
•More than
•Increased
•Plus
•Altogether

58. Words That Lead to Subtraction
•Decreased
•Less
•Difference
•Minus
•How many more

59. Words That Lead to
Multiplication
•Product
•Twice
•How many times
•Multiplied

60. Words That Lead to Division
•Quotient
•Shared
•Divide by

61. Write Algebraic Expressions
for These Word Phrases
•Ten more than a number
•A number decrease by 5
•6 less than a number
•A number increased by 8
•The sum of a number & 9
•4 more than a number
n + 10
w - 5
x - 6
n + 8
n + 9
y + 4

62. Write Algebraic Expressions
for These Word Phrases
•A number plus 2
•A number decrease by 1
•31 less than a number
•A number increased by 7
•The sum of a number & 6
•9 more than a number
s + 2
k - 1
x - 31
b + 7
n + 6
z + 9

63. Write Algebraic Expressions
for These Word Phrases
•The product of 4 and
another number is 12
•10 plus 3 times a number
is equal to 25
•A number multiplied by 7
is equal to 21
•Twice a number is equal 6
4s = 12
10 + 3x = 25
7b = 21
2n = 6

64. Write Algebraic Expressions
for These Word Phrases
•The quotient of 20 and
another number is 5
•A number divided by 3 is
equal to 12
•A quarter of a number is
erqual to 32
20
y = 5
x
3 = 12
C
4 = 32

65. •Xoliswe subtracts 120 from a
certain number, the answer is 31
•Alex adds 75 to a number, the
answer is 216.
120 - f = 31
75 + y = 216

66. •Sipho multiplies a number by 8
the answer is 88.
•A certain number is divided by
10, the answer is 120
8b = 88
y
10 = 120

67. Definitions
•Simplify – Combine like terms
and complete all operations
m = 2
•m + 8 + m = 2m + 8
•(2 x m) + 8 = 2m + 8
•4 x m = 4m
•6 ÷ m = 6
m

68. Write an Algebraic Expression
for These Situations
• Scott’s brother is 2 years younger than
Scott.
• The sum of two numbers is 12
• The difference between two numbers is 5
s - 2
v + c = 12
m – n = 5

69. Evaluate each algebraic
expression when x = 10
•x + 8 =
•x + 49
•x + x
•x - x
•x - 7
•42 - x
18
59
20
0
3
32

70. Complete This Table
n n - 3
5
10
21
32
2
7
18
29

71. Complete This Table
x x + 6
5
10
21
32
11
16
27
38