Unit 4. Day 17.

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

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

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

𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐶∗: 5𝑚 + 8 = 2𝑚 +29 𝐸𝑥𝑎𝑚𝑝𝑙𝑒 𝐷∗: 10 + 7𝑛 = 4𝑛 − 14

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

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

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

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

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

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 = =