1. Unit 3. Day 9.

2. Please get out paper for today’s lesson
Name
Date
Period
Topic: Solving equations with rational numbers (practice)
7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

3. Word Problems:
1) Model
with an equation
2) Solve

4. Two minutes to find the answer
Example A: For his birthday, Nasir and three of his friends went to a movie at the BX. They each got a ticket for $8.00 and the same snack from the concession stand. If Nasir’s mom paid $48 for the group’s tickets and snacks, how much did each snack cost?
Two minutes to find the answer
− 13 3 𝑥=

5. Example A: For his birthday, Nasir and three of his friends went to a movie at the BX. They each got a ticket for $8.00 and the same snack from the concession stand. If Nasir’s mom paid $48 for the group’s tickets and snacks, how much did each snack cost? 4 = 48 𝑠 𝑠 𝑠 𝑠 8 8 8 8
𝑠+8
𝑠+8
𝑠+8
𝑠+8
𝑠+8
𝑠+8
𝑠+8
𝑠+8

6. 4 𝑠+8 =48 =48 4𝑠 + 32 Each snack cost $4 4𝑠 = 16 4 4 𝑠 = 4 −32 −32
Example A: For his birthday, Nasir and three of his friends went to a movie at the BX. They each got a ticket for $8.00 and the same snack from the concession stand. If Nasir’s mom paid $48 for the group’s tickets and snacks, how much did each snack cost?
4 𝑠+8 =48
=48 4𝑠 + 32
−32
−32
Each snack cost $4 4𝑠 = 16 4 4 𝑠 = 4

7. Aaron was babysat for 5 hours
Example B: The cost of a babysitting service on a cruise is $10 for the first hour and $12 for each additional hour. If the total cost of babysitting baby Aaron was $58, how many hours was Aaron at the sitter? + ∙ ℎ = 58
10+12ℎ=58
−10
−10 =
12ℎ 48 58 12 12 10 10 12 12 12 12 12 12 12 12 ℎ = 4
Aaron was babysat for 5 hours
Hour 1
Hour 2
Hour 3
Hour 4
Hour 5

8. Each afternoon he must work 5 hours
Example C: Eric’s father works two part-time jobs, one in the morning and one in the afternoon. He needs to work 40 hours each 5-day workweek to pay his bills. If his schedule is the same each day (M-F), and he works 3 hours each morning, how many hours does he need to work in the afternoon? 5 = 40
Each afternoon he must work 5 hours 15 + 5𝑎 = 40
−15
−15 5𝑎 = 25 40 5 5
3+𝑎 3 + 𝑎
3+𝑎
3+𝑎
3+𝑎
3+𝑎
3+𝑎
3+𝑎
3+𝑎
3+𝑎 𝑎 = 5
Day 1
Day 2
Day 3
Day 4
Day 5

9. Example D: Write an equation and solve.
The perimeter of a rectangle is 54 cm. Its length is 16 cm. What is its width? 𝑙
11 cm 𝑤 𝑤 𝑙
𝑃=𝑤+𝑤+𝑙+𝑙
𝑃=2 𝑤+𝑙
54= 54 𝑃 =
𝑤+𝑤+ + 16 𝑙 16 𝑙
54=2 𝑤+16
54= 2𝑤
+ 32 2𝑤
+ 32
−32
−32
−32
−32 22 = 2𝑤 22 = 2𝑤 2 2 2 2 11 = 𝑤 11 = 𝑤

11. 6th Grade Solving: 7th Grade Solving:
CCSS.MATH.CONTENT.6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
7th Grade Solving:
CCSS.MATH.CONTENT.6.EE.B.7 Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently.

12. 6th Grade Solving: 7th Grade Solving:
Equations of the form x + p = q  and  px = q 
where  p, q and x are all nonnegative rational numbers.
7th Grade Solving:
Equations of the form  px + q = r  and  p(x + q) = r
where p, q, and r are specific rational numbers.

13. 7th Grade Solving: px + q = r p(x + q) = r
Equations of the form  px + q = r  and  p(x + q) = r
where p, q, and r are specific rational numbers.
px + q = r
p(x + q) = r
− 3 4
3 4
1 2
− 2 3
99 100
− 1 2
2 7
− 6 5
− 3 4
1 4
−4.62 −8
−2.3 𝑝 2 𝑥 + −1 𝑞 = 𝑟 −8
−.77
−4.62 −2 𝑝 𝑥+ 𝑞 = 𝑟
3.9
0.5 11 5
0.8
2.1 2
1.1
0.1 −2 5

15. 1)
4𝑥+2 =−9 −2 −2 4𝑥 =
−11 4 4
− 11 4 𝑥 =

16. − 2 3 𝑥 = 7 8
(2)
7 8 − 5 6
21 24 − 20 24
1 24
− 5 6
− 5 6 = =
− 2 3 𝑥
1 24 ∙ =
− 2 3
− 2 3
1 24
− 2 3 𝑥= ÷
1 24
− 3 2 3 3
− 1 16
𝑥 = ∙ = − = = 48
2∙2∙2∙2∙3

17. (3)
1.5𝑥 + −0.05 =−2.3
+0.05
+0.05 . 1 5 = −
1.5𝑥
2.25
1 5 .
2 2 5 . 5
1.5
1.5 −
1 5 7 −
7 0
𝑥 = −
1.5 2 1
2.3 −
0.05 2 . 2 5

18. 5 6 𝑥 = 3 5
5 6 𝑥+0.4 = 3 5
4 10
2 5
(4)
0.4
− 2 5
− 2 5
5 6 𝑥
1 5 ∙ =
5 6
5 6
1 5
5 6 𝑥= ÷
1 5
6 5 6
2∙3
6 25
𝑥 = ∙ = − = = 25
5∙5

19. −3 𝑥+5 =−7 −3 𝑥+5 =−7 =−7 −3 𝑥+5 =−7 −3 −3 −3𝑥 −15 7 3 𝑥+5 = −3𝑥 = 85)
−3 𝑥+5 =−7
−3 𝑥+5 =−7
=−7
−3 𝑥+5 =−7 −3 −3
−3𝑥
−15
+15
+15
7 3
𝑥+5 =
−3𝑥 = 8 −3 −3
− 8 3 𝑥 =

20. 6)
−7+ 3 5
− 2 3 𝑥 =−7 −
− 2 3 𝑥
− 18 30
− 3 5
=−7
+ 3 5
+ 3 5 − 35 3
− 2 3 𝑥 =
− 32 5
− 32 5
− 2 3
− 2 3
− 32 5 ÷− 2 3
− 32 5 ∙− 3 2
96 10
48 5 𝑥 = = = =

21. 7)
−0.6 𝑥+2.4 =8.4
−0.6 𝑥+2.4 =8.4
−0.6 𝑥+2.4 =8.4
−0.6
−0.6
−0.6𝑥
−1.44
8.4 =
+1.44
+1.44
𝑥+2.4 =
−14
−2.4
−2.4
−0.6𝑥 =
9.84
−0.6
−0.6 𝑥 =
−16.4 𝑥 =
−16.4 1 6 . 4 . 2
0 6 .
9 8 4 8 4
2 . 4 − 6 ×
0 . 6 3 −
3 6
1 4 . 4 2

22. 8)
−3 𝑥 =3.6
− 6 5
18 5
36 10
−3𝑥 =
+ 6 5
+ 6 5
24 5
−3𝑥 = −3 −3
24 5 ÷− 3 1
24 5 ∙− 1 3
− 24 15
− 8 5 𝑥 = = = =

23. 6th Grade Solving: 7th Grade Solving: 8th Grade Solving:
Equations of the form x + p = q  and  px = q 
where  p, q and x are all nonnegative rational numbers.
7th Grade Solving:
Equations of the form  px + q = r  and  p(x + q) = r
where p, q, and r are specific rational numbers.
8th Grade Solving:
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

24. 9)
1 4 𝑥 − 7 8 𝑥− =− 9 10
− 7 8 𝑥− =− 9 10
1𝑥 8
1 8 𝑥
15 12
5 4 +
− 3 4 𝑥
−6 8 𝑥
+ 6 10
− 9 10 =
− 6 10
− 6 10
− 3 4 𝑥
− 3 2
− 15 10 =
− 3 2
− 4 3
− 3 4
12 6 𝑥 = ÷ ∙ = = 2
− 3 4
− 1 2