1. Unit 4. Day 17.

2. Today’s Lesson
1) Equations with a variable on BOTH SIDES!
2) Modeling Practice

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

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

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

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

7. 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

8. 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

9. 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

11. Today’s Lesson
1) Equations with a variable on BOTH SIDES!
2) Modeling Practice

12. Each shelf is 2 ft. in length 𝑠 𝑠
Example G: 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

13. Example H: 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 = =