Unit 4. Day 8.

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

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

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

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

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÷8 100 100 100÷100 → =1

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

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+ 3 4 = 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− 3 7 =− 1 5 − 5 6 𝑥+ 1 2 =− 1 4

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

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

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*:

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

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

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

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

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

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

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

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

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

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

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

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

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

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 =