1. Unit 4. Day 8.

2. Today’s Lesson 1) Three important questions 2) Division review
3) Solving Equations

3. A math “sentence” with an equal sign
Q: What is an equation? A:
A math “sentence” with an equal sign
3𝑥 + 4 = 78
3 5−𝑦 =6−3𝑦
6 𝑎+5 =7−9𝑎
Q: What does it mean to solve an equation? A:
To find the value of the variable
Q: How do we solve an equation? A:
Isolate the variable

5. Today’s Lesson 1) Three important questions 2) Division review
3) Solving Equations

6. 11 𝑦 8 2 8÷2 11÷𝑦 3 7 𝑎+𝑏 2 3÷7 𝑎+𝑏 ÷2 6𝑥 6 𝑥 6 6𝑥÷6 𝑥÷6 10𝑚 10 10𝑚÷10
𝐻𝑜𝑤 𝑡𝑜 𝑏𝑒 𝑐𝑜𝑜𝑙 𝑖𝑛 𝐴𝑙𝑔𝑒𝑏𝑟𝑎 𝑤𝑖𝑡ℎ 𝐷𝑖𝑣𝑖𝑠𝑖𝑜𝑛
11 𝑦
8 2
8÷2
11÷𝑦
3 7
𝑎+𝑏 2
3÷7
𝑎+𝑏 ÷2
6𝑥 6
𝑥 6
6𝑥÷6
𝑥÷6
10𝑚 10
10𝑚÷10

7. 𝐷𝑜 𝑛 ′ 𝑡 𝑓𝑜𝑟𝑔𝑒𝑡 𝑟𝑒𝑑𝑢𝑐𝑖𝑛𝑔‼‼‼
8 2
3 3
8÷2 → =4
3÷3 → =1
9 4
= 9 4
9÷4 →
11 11
11÷11 → =1
12 8 →
= 3 2
12÷8
100÷100 → =1

9. Today’s Lesson 1) Three important questions 2) Division review
3) Solving Equations 6th  7th

10. 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.
𝑥 = 7 8
1 2 𝑥 = 6 5
𝑥+4 =7
3𝑥 =12
CCSS.MATH.CONTENT.7.EE.B.4.A 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.
−2 𝑥−7 =5
3𝑥+4 =−8
1 2 𝑥− =− 1 5
− 5 6 𝑥 =− 1 4

11. Example A: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 x. 1
3𝑥=15 𝑥 = 5 ∙ 3 3
Check:
=15 5
15=15

12. “Reducing” vs. “Canceling”
Example A:
𝑥+3 =15 𝑥 + = 12 1
3𝑥=15 𝑥 = 5 ∙ −3 −3 3 3
“Reducing” vs. “Canceling”

13. 4𝑤=24 5𝑒=30 2 3 𝑓=8 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 Example B*: Example C*:
𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
Example B*:
4𝑤=24
Example C*:
5𝑒=30
2 3 𝑓=8
Example D*:

14. Example B*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 w. 1
4𝑤=24 𝑤 = 6 ∙ 4 4
Check
=24 6
24=24

15. Example C*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑒 .
5𝑒=30 𝑒 = 6 ∙ 5 5
Check
=30 6
30=30

16. 2 3 𝑓=8 𝑓 = Example D*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑓 . ∙ 12 1 2 3 2 3 8 1 2 3 ÷ 8 1 3 2
24 2 𝑓= ∙ = = 12

17. − − − − 3𝑝=18 𝑝 = −6 Example E: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑝. 7th Grade 6th Grade −3 −3
Check
− =18 −6
18=18

18. 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
Example F*:
−2𝑚=−16
Example G*:
36=−6𝑛

19. Example F*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑝.
−2𝑚=−16 𝑚 = 8 −2 −2
Check
− =−16 8
−16=−16

20. Example G*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑝. −6
36=−6𝑛 = 𝑛 −6 −6
Check
36=−6 −6
36=36

21. 30 8 8𝑛=30 𝑛 = Example H: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑛 . ∙ 8 8 𝑛= 15 4 Check 8 =30
=30
120 4 =30
30=30

22. Solve for the variable.
Example I*:
−6ℎ = 20
Example J*:
−𝑥 =8

23. −6ℎ = 20 ℎ = Example I*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 ℎ . ∙ −6 −6 − 20 6 ℎ=− 10 3 −3 1 3
Check
− 10 3
− =20
60 3 =20
20=20

24. Example J*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 ℎ .
− 𝑥 = 8 1 𝑥 = ∙ −8 −1 −1

25. Example K: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 x. 3 1 𝑥 3
𝑥 3 = 9 27
𝑥÷3=9 =
Check
3 =9 27
9=9

26. 𝑦 −44 = 4 4 𝑦 4 =−11 𝑦÷4=−11 Example L*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 y. Check 4 =−11 −44
𝑦 4 =−11
−44
𝑦÷4=−11 =
Check
4 =−11
−44
−11=−11

27. Example M: Write an equation. Then solve the equation.
Mr. Jordan wants to take his wife on a fancy date to see a Cirque Du Soleil show. The fancy date will cost €480. If he saves €36 each month, in how many months will he have enough for the date? 36 𝑚 = ∙
480
36𝑚 = 480 36 36
𝑚= 40 3
480 36 𝑚 =
𝑚=13 1 3
2∙2∙2∙2∙2∙3∙5 2∙2∙3∙3 𝑚 =