1. Unit 3. Day 10.

2. Please get out paper for today’s lesson
Name
Date
Period
Topic: Solving equations with a variable on both sides
8.EE.C.7.A Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

3. Today’s Lesson
1) Equations with a variable on BOTH SIDES!
2) How many answers are there?!?!??!
3) Modeling Practice

4. 𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐴: 𝑆𝑜𝑙𝑣𝑒.
6𝑥+5=2𝑥+29
−2𝑥
−2𝑥 4𝑥
+ 5 = 29 −5 −5 4𝑥 = 24 4 4 𝑥 = 6

5. 𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐵: 𝑆𝑜𝑙𝑣𝑒.
𝑦−7=−3𝑦+9
+3𝑦
+3𝑦 4𝑦 −7 = 9 +7 +7 4𝑦 = 16 4 4 𝑦 = 4

6. 𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐶∗: 5𝑚 + 8 = 2𝑚 +29
𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐷∗: 𝑛 = 4𝑛 − 14

7. 𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐶∗: 𝑆𝑜𝑙𝑣𝑒.
5𝑚+ 8=2𝑚+29
−2𝑚
−2𝑚 3𝑚 +8 = 29 −8 −8 3𝑚 = 21 3 3 𝑚 = 7

8. 𝑛 = −8 = 10+7𝑛 =4𝑛−14 −4𝑛 −4𝑛 10 +3𝑛 = −14 −10 −10 3𝑛 −24 3 3
𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐷∗: 𝑆𝑜𝑙𝑣𝑒.
10+7𝑛 =4𝑛−14
−4𝑛
−4𝑛 10
+3𝑛 =
−14
−10
−10 3𝑛 =
−24 3 3 𝑛 = −8

9. 2𝑥+4 =6𝑥+40 2𝑥+4 =6𝑥+40 −6𝑥 −2𝑥 −2𝑥 −6𝑥 4 = 4𝑥 + 40 −40 −40 −4𝑥 + 4 =
𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐸: 𝑆𝑜𝑙𝑣𝑒.
2𝑥+4 =6𝑥+40
2𝑥+4 =6𝑥+40
−6𝑥
−2𝑥
−2𝑥
−6𝑥 4 = 4𝑥
+ 40
−40
−40
−4𝑥
+ 4 = 40 −4 −4
−36 = 4𝑥 4 4
−4𝑥 = 36 −4 −4 𝑥 = −9 −9 = 𝑥

10. 3𝑘−6=8𝑘+4 3𝑘−6=8𝑘+4 −8𝑘 −8𝑘 −3𝑘 −3𝑘 −6 = 5𝑘 + 4 −4 −4 −5𝑘 −6 = 4 +6 +6
𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐹∗: 𝑆𝑜𝑙𝑣𝑒.
3𝑘−6=8𝑘+4
3𝑘−6=8𝑘+4
−8𝑘
−8𝑘
−3𝑘
−3𝑘 −6 = 5𝑘
+ 4 −4 −4
−5𝑘 −6 = 4 +6 +6
−10 = 5𝑘 5 5
−5𝑘 = 10 −5 −5 𝑘 = −2 −2 = 𝑘

12. Today’s Lesson
1) Equations with a variable on BOTH SIDES!
2) How many answers are there?!?!??!
3) Modeling Practice

13. 8.EE.C.7.A Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.
𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐹:
3𝑘−6=8𝑘+4
−8𝑘
−8𝑘
3( )−6=8( )+4 −5 −2 3 −5 −2 3
−5𝑘 −6 = 4 +6
−15−6=−40+4
−6−6=−16+4
9−6=24+4 +6
0−6=0+4
−21=−36
−12=−12
−6=4
3=28
−5𝑘 = 10 −5 −5 𝑘 = −2

14. 8.EE.C.7.A Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.
𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐺:
2𝑛+3=2𝑛+3
−2𝑛
−2𝑛
=2( )+3 −2 −5 3 −2 −5 3 3 = 3
−10+3=−10+3
−4+3=−4+3
6+3=6+3
0+3=0+3
−7=−7
−1=−1
3=3
9=9 𝑛 = ?

15. 8.EE.C.7.A Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.
𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐻:
−4𝑎+5=−4𝑎+6
+4𝑎
+4𝑎
− =−4( )+6 −5 −2 −5 −2 3 3 5 = 6
−12+5=−12+6
20+5=20+6
8+5=8+6
0+5=0+6
−7=−6
13=14
5=6
−21=−36 𝑎 = ?

17. Today’s Lesson
1) Equations with a variable on BOTH SIDES!
2) How many answers are there?!?!??!
3) Modeling Practice

18. Each shelf is 2 ft. in length 𝑠 𝑠
Example I: Henry is using a total of 16 ft. of lumber to make a bookcase. The left and right sides of the bookcase are 4 ft. high. How long is each shelf? 𝑠 𝑠 4 + 2 = 16 𝑠 𝑠
4𝑠+8=16 −8 −8 4 4 4 4 𝑠 𝑠 4𝑠 = 8
Each shelf is 2 ft. in length 4 4 𝑠 𝑠 𝑥 = 2

19. Example J: Write and solve an equation.
Amy charges $7 an hour babysitting. She wants to buy a new pair of Jordan shoes that costs $130. If she already babysat for 5 hours, how many more hours does she need to work to buy the shoes? 7
130 5 ℎ + =
7 ℎ+5 =130
7∙5 +
7∙ℎ =
130 7ℎ
+ 35 =
130 35
+ 7ℎ =
130
−35
−35
−35
−35 7ℎ = 95 7ℎ = 95 7 7 7 7
95 7
13 4 7 =
95 7
13 4 7 ℎ = ℎ = =