1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Evaluate each expression for x = 12. 1. x + 2 2. 3. x – 8 4. 10x – 4
Warm Up
Evaluate each expression for x = 12.
1. x + 2 2.
3. x – 8
4. 10x – 4
5. 2x + 12
6. 5x + 7 14 x 4 3 4
116 36 67

3. Problem of the Day
Alicia buys buttons at a cost of 8 for $20. She resells them for $5 each. How many buttons does Alicia need to sell for a profit of $120?
48 buttons

4. Learn to determine whether a number is a solution of an equation.

5. Vocabulary
equation
solution

6. Ella has 22 CDs. This is 9 more than her friend Kay has.
This situation can be written as an equation.
An equation is a mathematical statement
that two expressions are equal in value.
An equation is like a balanced scale.
Number of
CDs Ella has 22
is equal to =
9 more than
Kay has
j + 9
Left expression
Right expression

7. Just as the weights on both sides of a balanced scale are exactly the same, the expressions on both sides of an equation represent exactly the same value.
When an equation contains a variable, a value of the variable that makes the statement true is called a solution of the equation.
22 = j j = 13 is a solution because 22 =
22 = j j = 15 is not a solution because 22 
Reading Math
The symbol ≠ means “is not equal to.”

8. Additional Example 1A: Determining Whether a Number is a Solution of an Equation
Determine whether the given value of the variable is a solution of t + 9 = 17. 26
t + 9 = 17
= 17 ?
Substitute 26 for t.
35 = 17 ? 
26 is not a solution of t + 9 = 17.

9. Additional Example 1B: Determining Whether a Number is a Solution of an Equation
Determine whether the given value of the variable is a solution of t + 9 = 17. 8
t + 9 = 17
8 + 9 = 17 ?
Substitute 8 for t.
17 = 17 ? 
8 is a solution of t + 9 = 17.

10.   Check It Out: Example 1
Determine whether each number is a solution of x – 5 = 12.
A. 22
x – 5 = 12
22 – 5 = 12 ?
Substitute 22 for x.
17 = 12 ? 
22 is not a solution of x – 5 = 12.
B. 8
x – 5 = 12
8 – 5 = 12 ?
Substitute 8 for x.
3 = 12 ? 
8 is not a solution of x – 5 = 12.

11. Additional Example 2: Writing an Equation to Determine Whether a Number is a Solution
Mrs. Jenkins had $32 when she returned home from the supermarket. If she spent $17 at the supermarket, did she have $52 or $49 before she went shopping?
You can write an equation to find the amount of money Mrs. Jenkins had before she went shopping. If m represents the amount of money she had before she went shopping, then m - 17 = 32.
$52
m – 17 = 32
= 32 ?
Substitute 52 for m.
35 = 32 ? 

12. Additional Example 2 Continued
Mrs. Jenkins had $32 when she returned home from the supermarket. If she spent $17 at the supermarket, did she have $52 or $49 before she went shopping?
You can write an equation to find the amount of money Mrs. Jenkins had before she went shopping. If m represents the amount of money she had before she went shopping, then m - 17 = 32.
$49
m – 17 = 32
= 32 ?
Substitute 49 for m.
32 = 32 ? 
Mrs. Jenkins had $49 before she went shopping.

13. Check It Out: Example 2
Mr. Rorke had $12 when he returned home from buying a hat. If he spent $47 at the hat store, did he have $61 or $59 before he bought the hat?
You can write an equation to find the amount of money Mr. Rorke had before he purchased a hat. If m represents the amount of money he had before he purchased a hat, then m – 47 = 12.
$61
m – 47 = 12
= 12 ?
Substitute 61 for h.
14 = 12 ? 

14. Check It Out: Example 2 Continued
Mr. Rorke had $12 when he returned home from buying a hat. If he spent $47 at the hat store, did he have $59 or $61 before he bought the hat?
You can write an equation to find the amount of money Mr. Rorke had before he purchased a hat. If m represents the amount of money he had before he purchased a hat, then m – 47 = 12.
$59
m – 47 = 12
= 12 ?
Substitute 59 for h.
12 = 12 ? 
Mr. Rorke had $59 before he purchased a hat.

15. Additional Example 3: Deriving a Real-World Situation from an Equation
Which problem situation best matches the equation 5 + 2x = 13?
Situation A:
Admission to the county fair costs $5 and rides cost $2 each. Mike spent a total of $13. How many rides did he go on?
$5 for admission
$2 per ride x
Mike spent $13 in all, so 5 + 2x = 13. Situation A matches the equation.

16. Additional Example 3 Continued
Which problem situation best matches the equation 5 + 2x = 13?
Situation B:
Admission to the county fair costs $2 and rides cost $5 each. Mike spent a total of $13. How many rides did he go on?
The variable x represents the number of rides that Mike bought.
$5 per ride x
Since 5x is not a term in the given equation, Situation B does not match the equation.

17. Check It Out: Example 3
Which problem situation best matches the equation x = 25?
Situation A:
Admission to the baseball game costs $4 and souvenir hats cost $13 each. Trina spent a total of $25. How many souvenir hats did she buy?
The variable x represents the number of souvenir hats Trina bought.
$13 per souvenir hat x
Since 13x is not a term in the given equation, Situation A does not match the equation.

18. Check It Out: Example 3 Continued
Which problem situation best matches the equation x = 25?
Situation B:
Admission to the baseball game costs $13 and souvenir hats cost $4 each. Trina spent a total of $25. How many souvenir hats did she buy?
$13 for admission
$4 per souvenir hat x
Trina spent $25 in all, so x = 25. Situation B matches the equation.

19. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

20. Lesson Quiz
Determine whether the given value of the variable is a solution of 5 + x = 47.
1. x = x = 52
Determine whether the given value of the variable is a solution of 57 – y = 18.
3. y = y = 39
5. Kwan has 14 marbles. This is 7 more than Drue has. Does Drue have 21 or 7 marbles?
yes no no
yes 7

21. Lesson Quiz for Student Response Systems
1. Identify the value of the variable that is a solution of 7 + x = 52.
A. x = 45
B. x = 55
C. x = 50
D. x = 60

22. Lesson Quiz for Student Response Systems
2. Identify the value of the variable that is a solution of 8 + z = 53.
A. z = 57
B. z = 49
C. z = 53
D. z = 45

23. Lesson Quiz for Student Response Systems
3. Identify the value of the variable that is a solution of 71 – n = 11.
A. n = 40
B. n = 60
C. n = 50
D. n = 70

24. Lesson Quiz for Student Response Systems
4. Identify the value of the variable that is a solution of 50 – y = 9.
A. y = 41
B. y = 52
C. y = 48
D. y = 59

25. Lesson Quiz for Student Response Systems
5. Rita has 18 storybooks. This is nine more than Reena has. Does Reena have 3, 9, 18, or 27 storybooks?
A. 27 storybooks
B. 18 storybooks
C. 9 storybooks
D. 3 storybooks