1. Unit 3. Day 3.

2. Please get out paper for today’s lesson
Name
Date
Period
Topic: Practice with Equivalent Expressions
Use properties of operations to generate equivalent expressions

3. Today’s Lesson 1) Practice with Expressions
2) Legality of Math Equations
3) 6th Grade Solving
4) 7th Grade Solving

4. Commercial Break #1 2 2𝑥 ∙ 𝑥 3𝑥 4 3 4 3 4 𝑥 3 4𝑥 1 ∙ 𝑥 1 7 1 1 1 7 𝑥
𝑥 7
𝑥 7 ∙ 𝑥

5. Commercial Break #1
5𝑛 6
5 6 𝑛
− 7𝑚 8
− 7 8 𝑚
1𝑎 2
1 2 𝑎
𝑎 2

6. Example A: Rewrite the expressions by collecting like terms
2 3 𝑥
2 3 𝑥− 3 4 𝑦+4𝑥− 𝑦 5 + 5𝑥 6
− 3 4 𝑦
+ 5𝑥 6
− 𝑦 5
+ 4𝑥
11 2 𝑥
− 𝑦
2 3 𝑥 𝑥 𝑥
− 3 4 𝑦
− 1 5 𝑦 15
6 𝑥 𝑥 𝑥 4 24 5 33
11 2 𝑥
− 20 𝑦− 20 𝑦 4
− 𝑦 = 6 𝑥 = =

7. Example B*: Rewrite the expressions by collecting like terms
5 8 − 𝑛 6 +3𝑛−1 3 4 − 3 2 𝑛
5 8
− 1 3 4
− 𝑛 6
− 3 2 𝑛
+ 3𝑛
− 9 8
− 9 8
4 3 𝑛
4 3 𝑛 + +
5 8
− 7 4
− 1 6 𝑛 𝑛
− 3 2 𝑛 8
8 − 8 5 14
− 6 𝑛 𝑛 − 6 𝑛 1 18
6 𝑛 −9 9 = 8 =

9. Commercial Break #2
2𝑥 3
2𝑥+5 3
5 3 +
8 11 − 5𝑦 11
8−5𝑦 11

10. Commercial Break #2 8𝑥 − 6 8𝑥−6 12 8𝑥 12 −6 12 12 12 8 12 𝑥 − 6 12
2 3 𝑥
− 1 2

11. Example C: Rewrite the following expression in standard form
2 3𝑥−4 6 − 5𝑥+2 8 4
6 − 5𝑥+2 8 6𝑥
− 8 3 4 3
24𝑥−32
24𝑥
−32
15𝑥+6
15𝑥
+ 6
24 − −
−15𝑥 −6 9𝑥
−38
9𝑥 24
38 24
3 8 𝑥
− 19 12
24𝑥
−32 24 = 24 = − =

12. Example D*: Rewrite the following expression in standard form
2 5𝑔−1 4 − 2𝑔+3 6 3 2
4 − 2𝑔+3 6
10𝑔
− 2 3 2
30𝑔−6
30𝑔 −6
4𝑔+6 4𝑔
+ 6
12 − −
−4𝑔 −6
26𝑔
−12
26𝑔 12 −6
12 12
13 6 𝑔
30𝑔 = 12 = − 12 = −1

14. Today’s Lesson 1) Practice with Expressions
2) Legality of Math Equations
3) 6th Grade Solving
4) 7th Grade Solving

15. Q: What is an equation? A: A math “sentence” with an equal sign
3𝑥 + 4 = 78
3 5−𝑥 =6−3𝑥
5=2+3
6 𝑥+5 =7−9𝑚
𝑥+4=2−13.9

16. 4 = 4 6 = 6 3 = 3 15 = 15 5 = 5 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑡𝑟𝑢𝑒? 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒?
Legality of Math Equations
4 = 4
𝐼𝑠 𝑡ℎ𝑖𝑠 𝑡𝑟𝑢𝑒? +2 +2
6 = 6
𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒? −3 −3 5 5
3 = 3
𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒?
15 = 15
𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒? 3 3
5 = 5
𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒?

17. 8 = 8 4 = 4 2 = 2 7 = 7 49 = 49 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑡𝑟𝑢𝑒? 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒?
Legality of Math Equations
8 = 8
𝐼𝑠 𝑡ℎ𝑖𝑠 𝑡𝑟𝑢𝑒? 2 2
4 = 4
𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒?
2 = 2
𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒? +5 +5
7 = 7 2 2
𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒?
49 = 49
𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒?

19. Today’s Lesson 1) Practice with Expressions
2) Legality of Math Equations
3) 6th Grade Solving
4) 7th Grade Solving

20. 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+𝑝 =𝑞
𝑝𝑥=𝑞
𝑥+4 =7
3𝑥 =12
𝑥 = 7 8
1 2 𝑥 = 6 5

21. 𝑝𝑥+𝑞 =𝑟 𝑝𝑥=𝑞 1 𝑥−4 =7 3𝑥 =−12 3 𝑥+0 =−12 −2 𝑥−7 =5 3𝑥+4 =−8
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.
𝑝𝑥+𝑞 =𝑟
𝑝𝑥=𝑞 1
𝑥−4 =7
3𝑥 =−12
3 𝑥+0 =−12
−2 𝑥−7 =5
3𝑥+4 =−8
1 2 𝑥− =− 1 5
− 5 6 𝑥 =− 1 4

22. 𝑥+4 = 7 𝑥+4 = 7 𝑥 = 3 𝑥 𝑥+4 = 7 = + −4 −4 Example 6th: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑥. +
Check:
+4=7 3
𝑥+4 = 7
𝑥+4 = 7 𝑥 = + 3
7=7 −4 −4 𝑥
𝑥+4 = 7 = + + + + + + + + + + + − − − − − − − −

23. Example 6th: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑦.
𝑦 = 3 8
2 8 𝑦 =
− 1 8
− 1 8
1 4

24. Example 6th: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 w. 1
4𝑤=24 𝑤 = 6 ∙ 4 4
Check
=24 6
24=24

25. Example 6th: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑛 .
3 4 𝑛= 9 10 𝑛 = ∙
3 4
3 4
9 10 ÷ 3 4
𝑛= 15 4
9 10
4 3
36 30
6 5 ∙ = =

27. Today’s Lesson 1) Practice with Expressions
2) Legality of Math Equations
3) 6th Grade Solving
4) 7th Grade Solving

28. 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒.
𝑎 =− 1 5
Example E*:
𝑛 − = 1 3
Example F*:

29. Example E*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑎.
𝑎 =− 1 5
− 3 5 𝑎 =
− 2 5
− 2 5

30. Example F*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑛.
𝑛 − = 1 3
5 9 𝑛 =
+ 2 9
+ 2 9

31. 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
−15+𝑏=−4
Example G*:
−31=𝑑−6
Example H*:

32. −15+𝑏=−4 𝑏 = 11 +15 +15 Example G*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑏. Check: −15+ =−4 11
− =−4 11
−15+𝑏=−4
+15
−4=−4
+15 𝑏 = 11

33. −31=𝑑−6 −25 = 𝑑 +6 +6 Example H*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑑. Check: −31= −6 −25
−31= −6
−25
−31=𝑑−6 +6
−31=−31 +6
−25 = 𝑑

34. Example I: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑝.
−2𝑚=−16 𝑚 = 8 −2 −2
Check
− =−16 8
−16=−16

35. 2 7 𝑥 = 5 ∙ 𝑥 = 5 ÷ 2 7 𝑥 = 1 ∙ 𝑥 = 5 ∙ 1 𝑥 = = Example J: 2 7 2 7 2 7
35 2
5 1
7 2
35 2 𝑥 = ∙ =

36. − 1 3 𝑚 =8 − 2 3 𝑛 =8 −𝑝 =−7 Example K*: Example L*: Example M*:
Solve for the variable
− 1 3 𝑚 =8
Example K*:
− 2 3 𝑛 =8
Example L*:
Example M*:
−𝑝 =−7

37. − 1 3 𝑚 =8 ∙ 𝑚 = 8 1 − 3 𝑚 =8 ÷ 1 𝑚 = = −3 −3 − 1 3 − 1 3 − 1 3 𝑚 =
Example K*: ∙ 𝑚 = 8 −3 1 −3 − 3 𝑚 =8 ÷
− 1 3
− 1 3
− 1 3 𝑚 =
−24 1
8 1
− 3 1
− 24 1 𝑚 = ∙ =

38. − 2 3 𝑛 =8 ∙ 𝑛 = 8 ÷ − 2 3 𝑥 = 1 ∙ 𝑥 = 8 ∙ 1 𝑛 = = Example L*: − 2 3
− 3 2
− 3 2 ∙ 𝑥 = 8 ∙
− 24 2 1
8 1
− 3 2
− 24 2 𝑛 = ∙ = =
−12

39. Example M*:
− 𝑝 =−7 1𝑝 1 = 7 −1 −1 𝑝

40. Example N: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 x. 3 1 𝑥 3
𝑥 3 = 9 27
𝑥÷3=9 = Or
1 3 𝑥 = 9
1𝑥 3 = 9
𝑥 3 = 9 ∙
1 3
1 3
9 1
1 3
3 1
27 1 𝑥 = ÷ ∙ = 27