P = (4.25n) - 35.23

1. Introduction
to Equations

2. Expression vs. Equation
Round 1

3. Expression vs. Equation
Round 1
• Equation is derived from the word equate, which
means one thing is the same as another thing.

4. Expression vs. Equation
Round 1
• Equation is derived from the word equate, which
means one thing is the same as another thing.
• Which symbol would you associate with equate?

5. Expression vs. Equation
Round 1
• Equation is derived from the word equate, which
means one thing is the same as another thing.
• Which symbol would you associate with equate?
• An = sign!

6. Expression vs. Equation
Round 1
• Equation is derived from the word equate, which
means one thing is the same as another thing.
• Which symbol would you associate with equate?
• An = sign!
• In Math, an equation always has an = sign.

7. Expression vs. Equation
Round 1
• Equation is derived from the word equate, which
means one thing is the same as another thing.
• Which symbol would you associate with equate?
• An = sign!
• In Math, an equation always has an = sign.
• Notice the word equation has part of the word equal.
So when you see equation, you know you must have an
equal sign.

8. = Equation Examples =
1
A = bh 2x − 3y + 5 = 8x − 13
2
1 ⎛ 2 ⎞ 7
y = 18 ⎜ a − 8b ⎟ + = 0
2 ⎝ 3 ⎠ 3
= =

9. = Equation Examples =
1
A = bh 2x − 3y + 5 = 8x − 13
2
1 ⎛ 2 ⎞ 7
y = 18 ⎜ a − 8b ⎟ + = 0
2 ⎝ 3 ⎠ 3
• Notice they all have an = sign.
= =

10. Expression vs. Equation
Round 2

11. Expression vs. Equation
Round 2
• Expression is derived from the word express,
which means high speed or quick.

12. Expression vs. Equation
Round 2
• Expression is derived from the word express,
which means high speed or quick.
• An expression does not have an = sign.

13. Expression vs. Equation
Round 2
• Expression is derived from the word express,
which means high speed or quick.
• An expression does not have an = sign.
• Notice the word expression has the word
express. This is a reminder we want to write the
expression as quickly as possible, which means no =.

14. Expression Examples
1 3 5 7
a− b+ c− 3x − 5y
2 4 6 8
−37
p −1.2x + 3.8y − 7.3

15. Expression Examples
1 3 5 7
a− b+ c− 3x − 5y
2 4 6 8
−37
p −1.2x + 3.8y − 7.3
• Notice no = sign.

16. Expression vs. Equation
Round 3

17. Expression vs. Equation
Round 3
• What is the relationship between an
equation and an expression?

18. Expression vs. Equation
Round 3
• What is the relationship between an
equation and an expression?
• Such as 3x - 5 = 8
and 23a + 5b

19. Expression vs. Equation
Round 3
• What is the relationship between an
equation and an expression?
• Such as 3x - 5 = 8
and 23a + 5b
• Notice each side of the equation is actually an
expression.

20. Expression vs. Equation
Round 3
• What is the relationship between an
equation and an expression?
• Such as 3x - 5 = 8
and 23a + 5b
• Notice each side of the equation is actually an
expression.
• An equation is made from 2 equal expressions.

21. How to build an equation...

22. How to build an equation...
• Start with 2 expressions

23. How to build an equation...
• Start with 2 expressions
1.3x − 2.5 7.4

24. How to build an equation...
• Start with 2 expressions
1.3x − 2.5 7.4
Expression

25. How to build an equation...
• Start with 2 expressions
1.3x − 2.5 7.4
Expression Expression

26. How to build an equation...
• Start with 2 expressions
1.3x − 2.5 7.4
• Put one expression on
Expression Expression
the left side of the =

27. How to build an equation...
• Start with 2 expressions
1.3x − 2.5 7.4
• Put one expression on
Expression Expression
the left side of the =
1.3x − 2.5 =

28. How to build an equation...
• Start with 2 expressions
1.3x − 2.5 7.4
• Put one expression on
Expression Expression
the left side of the =
• And the other on the
right side 1.3x − 2.5 =

29. How to build an equation...
• Start with 2 expressions
1.3x − 2.5 7.4
• Put one expression on
Expression Expression
the left side of the =
• And the other on the
right side 1.3x − 2.5 = 7.4

30. How to build an equation...
• Start with 2 expressions
1.3x − 2.5 7.4
• Put one expression on
Expression Expression
the left side of the =
• And the other on the
right side 1.3x − 2.5 = 7.4
• Now we have an
equation.

31. How to build an equation...
• Start with 2 expressions
1.3x − 2.5 7.4
• Put one expression on
Expression Expression
the left side of the =
• And the other on the
right side 1.3x − 2.5 = 7.4
• Now we have an
1.3x − 2.5 = 7.4
equation.
Equation

32. Identify as an Equation or Expression
• 3x + 2y = 5
• -3ab
• 987 = x
• ⅔p - ¾q = r
• V = lwh
• 987,456.23
• ⁵⁄₈ − ⁴⁄₇x

33. Identify as an Equation or Expression
• 3x + 2y = 5 • Equation
• -3ab
• 987 = x
• ⅔p - ¾q = r
• V = lwh
• 987,456.23
• ⁵⁄₈ − ⁴⁄₇x

34. Identify as an Equation or Expression
• 3x + 2y = 5 • Equation
• -3ab • Expression
• 987 = x
• ⅔p - ¾q = r
• V = lwh
• 987,456.23
• ⁵⁄₈ − ⁴⁄₇x

35. Identify as an Equation or Expression
• 3x + 2y = 5 • Equation
• -3ab • Expression
• 987 = x • Equation
• ⅔p - ¾q = r
• V = lwh
• 987,456.23
• ⁵⁄₈ − ⁴⁄₇x

36. Identify as an Equation or Expression
• 3x + 2y = 5 • Equation
• -3ab • Expression
• 987 = x • Equation
• ⅔p - ¾q = r • Equation
• V = lwh
• 987,456.23
• ⁵⁄₈ − ⁴⁄₇x

37. Identify as an Equation or Expression
• 3x + 2y = 5 • Equation
• -3ab • Expression
• 987 = x • Equation
• ⅔p - ¾q = r • Equation
• V = lwh • Equation
• 987,456.23
• ⁵⁄₈ − ⁴⁄₇x

38. Identify as an Equation or Expression
• 3x + 2y = 5 • Equation
• -3ab • Expression
• 987 = x • Equation
• ⅔p - ¾q = r • Equation
• V = lwh • Equation
• 987,456.23 • Expression
• ⁵⁄₈ − ⁴⁄₇x

39. Identify as an Equation or Expression
• 3x + 2y = 5 • Equation
• -3ab • Expression
• 987 = x • Equation
• ⅔p - ¾q = r • Equation
• V = lwh • Equation
• 987,456.23 • Expression
• ⁵⁄₈ − ⁴⁄₇x • Expression

40. • An equation is like a balance. The 2 side are always
equal.

41. Write an equation to represent ...
Each piece of candy costs $.55. The price of p pieces of
candy is $4.40.

42. Write an equation to represent ...
Each piece of candy costs $.55. The price of p pieces of
candy is $4.40.
• What are we equating?

43. Write an equation to represent ...
Each piece of candy costs $.55. The price of p pieces of
candy is $4.40.
• What are we equating?
• The total cost to the cost of the p pieces.

44. Write an equation to represent ...
Each piece of candy costs $.55. The price of p pieces of
candy is $4.40.
• What are we equating?
• The total cost to the cost of the p pieces.
• The amount charged for the candy is found by
multiplying the cost by how many bought.

45. Write an equation to represent ...
Each piece of candy costs $.55. The price of p pieces of
candy is $4.40.
• What are we equating?
• The total cost to the cost of the p pieces.
• The amount charged for the candy is found by
multiplying the cost by how many bought.
• Write the equation

46. Write an equation to represent ...
Each piece of candy costs $.55. The price of p pieces of
candy is $4.40.
• What are we equating?
• The total cost to the cost of the p pieces.
• The amount charged for the candy is found by
multiplying the cost by how many bought.
• Write the equation
• 4.40 = .55p

47. Write an equation to represent ...

48. Write an equation to represent ...
James made a withdrawal of d dollars from his checking
account. His old balance was $980.23, and his new balance
is $526.87.

49. Write an equation to represent ...
James made a withdrawal of d dollars from his checking
account. His old balance was $980.23, and his new balance
is $526.87.
• What does withdrawal mean?

50. Write an equation to represent ...
James made a withdrawal of d dollars from his checking
account. His old balance was $980.23, and his new balance
is $526.87.
• What does withdrawal mean?
• Withdrawal indicates something being taken away.

51. Write an equation to represent ...
James made a withdrawal of d dollars from his checking
account. His old balance was $980.23, and his new balance
is $526.87.
• What does withdrawal mean?
• Withdrawal indicates something being taken away.
• What are we equating?

52. Write an equation to represent ...
James made a withdrawal of d dollars from his checking
account. His old balance was $980.23, and his new balance
is $526.87.
• What does withdrawal mean?
• Withdrawal indicates something being taken away.
• What are we equating?
• Old balance minus withdrawal = New balance

53. Write an equation to represent ...
James made a withdrawal of d dollars from his checking
account. His old balance was $980.23, and his new balance
is $526.87.
• What does withdrawal mean?
• Withdrawal indicates something being taken away.
• What are we equating?
• Old balance minus withdrawal = New balance
• 980.23 − d = 526.87

54. Mya organized a pancake breakfast to raise
money to donate to the Habitat for Humanity.
She spent $35.23 on supplies and plans to
charge $4.25 for each breakfast. If P is the
profit and n is number of breakfast’s sold, what is the equation Mya
can use to determine her profit based on the number of breakfasts sold?

55. Mya organized a pancake breakfast to raise
money to donate to the Habitat for Humanity.
She spent $35.23 on supplies and plans to
charge $4.25 for each breakfast. If P is the
profit and n is number of breakfast’s sold, what is the equation Mya
can use to determine her profit based on the number of breakfasts sold?
• What is being equated?

56. Mya organized a pancake breakfast to raise
money to donate to the Habitat for Humanity.
She spent $35.23 on supplies and plans to
charge $4.25 for each breakfast. If P is the
profit and n is number of breakfast’s sold, what is the equation Mya
can use to determine her profit based on the number of breakfasts sold?
• What is being equated?
• The profit to the amount spent on supplies and amount charged.

57. Mya organized a pancake breakfast to raise
money to donate to the Habitat for Humanity.
She spent $35.23 on supplies and plans to
charge $4.25 for each breakfast. If P is the
profit and n is number of breakfast’s sold, what is the equation Mya
can use to determine her profit based on the number of breakfasts sold?
• What is being equated?
• The profit to the amount spent on supplies and amount charged.
• How do you show spent mathematically?

58. Mya organized a pancake breakfast to raise
money to donate to the Habitat for Humanity.
She spent $35.23 on supplies and plans to
charge $4.25 for each breakfast. If P is the
profit and n is number of breakfast’s sold, what is the equation Mya
can use to determine her profit based on the number of breakfasts sold?
• What is being equated?
• The profit to the amount spent on supplies and amount charged.
• How do you show spent mathematically?
• Spent indicates subtraction.

59. Mya organized a pancake breakfast to raise
money to donate to the Habitat for Humanity.
She spent $35.23 on supplies and plans to
charge $4.25 for each breakfast. If P is the
profit and n is number of breakfast’s sold, what is the equation Mya
can use to determine her profit based on the number of breakfasts sold?
• What is being equated?
• The profit to the amount spent on supplies and amount charged.
• How do you show spent mathematically?
• Spent indicates subtraction.
• Write the equation

60. Mya organized a pancake breakfast to raise
money to donate to the Habitat for Humanity.
She spent $35.23 on supplies and plans to
charge $4.25 for each breakfast. If P is the
profit and n is number of breakfast’s sold, what is the equation Mya
can use to determine her profit based on the number of breakfasts sold?
• What is being equated?
• The profit to the amount spent on supplies and amount charged.
• How do you show spent mathematically?
• Spent indicates subtraction.
• Write the equation
• P = 4.25n − 35.23

61. You try...

62. You try...
Aiden’s parent’s deposited $1250 into a savings account for him
when he was born and contributed $325 each year, y. Write the
equation that represents the total amount, T.

63. You try...
Aiden’s parent’s deposited $1250 into a savings account for him
when he was born and contributed $325 each year, y. Write the
equation that represents the total amount, T.
• What is being equated?

64. You try...
Aiden’s parent’s deposited $1250 into a savings account for him
when he was born and contributed $325 each year, y. Write the
equation that represents the total amount, T.
• What is being equated?
• The amounts put into the account and the total amount.

65. You try...
Aiden’s parent’s deposited $1250 into a savings account for him
when he was born and contributed $325 each year, y. Write the
equation that represents the total amount, T.
• What is being equated?
• The amounts put into the account and the total amount.
• What operation does deposited and contributed indicate?

66. You try...
Aiden’s parent’s deposited $1250 into a savings account for him
when he was born and contributed $325 each year, y. Write the
equation that represents the total amount, T.
• What is being equated?
• The amounts put into the account and the total amount.
• What operation does deposited and contributed indicate?
• Addition

67. You try...
Aiden’s parent’s deposited $1250 into a savings account for him
when he was born and contributed $325 each year, y. Write the
equation that represents the total amount, T.
• What is being equated?
• The amounts put into the account and the total amount.
• What operation does deposited and contributed indicate?
• Addition
• Write the equation

68. You try...
Aiden’s parent’s deposited $1250 into a savings account for him
when he was born and contributed $325 each year, y. Write the
equation that represents the total amount, T.
• What is being equated?
• The amounts put into the account and the total amount.
• What operation does deposited and contributed indicate?
• Addition
• Write the equation
• T = 1250 + 325y

69. You try...

70. You try...
Tyler receives $15 a week for school lunch, and the
cafeteria charges $2.35 for a lunch. If Tyler purchases a
lunch daily, write an equation to determine the amount
of money left, A, after d days.

71. You try...
Tyler receives $15 a week for school lunch, and the
cafeteria charges $2.35 for a lunch. If Tyler purchases a
lunch daily, write an equation to determine the amount
of money left, A, after d days.
• What are we equating?

72. You try...
Tyler receives $15 a week for school lunch, and the
cafeteria charges $2.35 for a lunch. If Tyler purchases a
lunch daily, write an equation to determine the amount
of money left, A, after d days.
• What are we equating?
• Amount left = money received minus amount spent
on lunch

73. You try...
Tyler receives $15 a week for school lunch, and the
cafeteria charges $2.35 for a lunch. If Tyler purchases a
lunch daily, write an equation to determine the amount
of money left, A, after d days.
• What are we equating?
• Amount left = money received minus amount spent
on lunch
• A = 15 − 2.35d

74. Key Points to Remember

75. Key Points to Remember
• An equation has an = sign, an expression does not.

76. Key Points to Remember
• An equation has an = sign, an expression does not.
• When writing equations, determine what 2 things
are being equated.

77. Key Points to Remember
• An equation has an = sign, an expression does not.
• When writing equations, determine what 2 things
are being equated.
• Look for key words to determine the operation to
use.