Unit 3. Day 9.

Please get out paper for today’s lesson Name Date Period -------------------------------------------------------- Topic: Solving equations with rational numbers (practice) 7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Word Problems: 1) Model with an equation 2) Solve

Two minutes to find the answer Example A: For his birthday, Nasir and three of his friends went to a movie at the BX. They each got a ticket for $8.00 and the same snack from the concession stand. If Nasir’s mom paid $48 for the group’s tickets and snacks, how much did each snack cost? Two minutes to find the answer − 13 3 𝑥=

Example A: For his birthday, Nasir and three of his friends went to a movie at the BX. They each got a ticket for $8.00 and the same snack from the concession stand. If Nasir’s mom paid $48 for the group’s tickets and snacks, how much did each snack cost? 4 = 48 𝑠 𝑠 𝑠 𝑠 8 8 8 8 𝑠+8 𝑠+8 𝑠+8 𝑠+8 𝑠+8 𝑠+8 𝑠+8 𝑠+8

4 𝑠+8 =48 =48 4𝑠 + 32 Each snack cost $4 4𝑠 = 16 4 4 𝑠 = 4 −32 −32 Example A: For his birthday, Nasir and three of his friends went to a movie at the BX. They each got a ticket for $8.00 and the same snack from the concession stand. If Nasir’s mom paid $48 for the group’s tickets and snacks, how much did each snack cost? 4 𝑠+8 =48 =48 4𝑠 + 32 −32 −32 Each snack cost $4 4𝑠 = 16 4 4 𝑠 = 4

Aaron was babysat for 5 hours Example B: The cost of a babysitting service on a cruise is $10 for the first hour and $12 for each additional hour. If the total cost of babysitting baby Aaron was $58, how many hours was Aaron at the sitter? + ∙ ℎ = 58 10+12ℎ=58 −10 −10 = 12ℎ 48 58 12 12 10 10 12 12 12 12 12 12 12 12 ℎ = 4 Aaron was babysat for 5 hours Hour 1 Hour 2 Hour 3 Hour 4 Hour 5

Each afternoon he must work 5 hours Example C: Eric’s father works two part-time jobs, one in the morning and one in the afternoon. He needs to work 40 hours each 5-day workweek to pay his bills. If his schedule is the same each day (M-F), and he works 3 hours each morning, how many hours does he need to work in the afternoon? 5 = 40 Each afternoon he must work 5 hours 15 + 5𝑎 = 40 −15 −15 5𝑎 = 25 40 5 5 3+𝑎 3 + 𝑎 3+𝑎 3+𝑎 3+𝑎 3+𝑎 3+𝑎 3+𝑎 3+𝑎 3+𝑎 𝑎 = 5 Day 1 Day 2 Day 3 Day 4 Day 5

Example D: Write an equation and solve. The perimeter of a rectangle is 54 cm. Its length is 16 cm. What is its width? 𝑙 11 cm 𝑤 𝑤 𝑙 𝑃=𝑤+𝑤+𝑙+𝑙 𝑃=2 𝑤+𝑙 54= 54 𝑃 = 𝑤+𝑤+ + 16 𝑙 16 𝑙 54=2 𝑤+16 54= 2𝑤 + 32 2𝑤 + 32 −32 −32 −32 −32 22 = 2𝑤 22 = 2𝑤 2 2 2 2 11 = 𝑤 11 = 𝑤

6th Grade Solving: 7th Grade Solving: 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. 7th Grade Solving: CCSS.MATH.CONTENT.6.EE.B.7 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. Solve equations of these forms fluently.

6th Grade Solving: 7th Grade Solving: Equations of the form x + p = q  and  px = q  where  p, q and x are all nonnegative rational numbers. 7th Grade Solving: Equations of the form  px + q = r  and  p(x + q) = r where p, q, and r are specific rational numbers.

7th Grade Solving: px + q = r p(x + q) = r Equations of the form  px + q = r  and  p(x + q) = r where p, q, and r are specific rational numbers. px + q = r p(x + q) = r − 3 4 3 4 1 2 − 2 3 99 100 − 1 2 2 7 − 6 5 − 3 4 1 4 −4.62 −8 −2.3 𝑝 2 𝑥 + −1 𝑞 = 𝑟 −8 −.77 −4.62 −2 𝑝 𝑥+ 𝑞 = 𝑟 3.9 0.5 11 5 0.8 2.1 2 1.1 0.1 −2 5

1) 4𝑥+2 =−9 −2 −2 4𝑥 = −11 4 4 − 11 4 𝑥 =

− 2 3 𝑥+ 5 6 = 7 8 (2) 7 8 − 5 6 21 24 − 20 24 1 24 − 5 6 − 5 6 = = − 2 3 𝑥 1 24 ∙ = − 2 3 − 2 3 1 24 − 2 3 𝑥= ÷ 1 24 − 3 2 3 3 − 1 16 𝑥 = ∙ = − = = 48 2∙2∙2∙2∙3

(3) 1.5𝑥 + −0.05 =−2.3 +0.05 +0.05 . 1 5 = − 1.5𝑥 2.25 1 5 . 2 2 5 . 5 1.5 1.5 − 1 5 7 − 7 0 𝑥 = − 1.5 2 1 2.3 − 0.05 2 . 2 5

5 6 𝑥 + = 3 5 5 6 𝑥+0.4 = 3 5 4 10 2 5 (4) 0.4 − 2 5 − 2 5 5 6 𝑥 1 5 ∙ = 5 6 5 6 1 5 5 6 𝑥= ÷ 1 5 6 5 6 2∙3 6 25 𝑥 = ∙ = − = = 25 5∙5

−3 𝑥+5 =−7 −3 𝑥+5 =−7 =−7 −3 𝑥+5 =−7 −3 −3 −3𝑥 −15 7 3 𝑥+5 = −3𝑥 = 8 5) −3 𝑥+5 =−7 −3 𝑥+5 =−7 =−7 −3 𝑥+5 =−7 −3 −3 −3𝑥 −15 +15 +15 7 3 𝑥+5 = −3𝑥 = 8 −3 −3 − 8 3 𝑥 =

6) −7+ 3 5 − 2 3 𝑥+ 9 10 =−7 − 7 1 + 3 5 − 2 3 𝑥 − 18 30 − 3 5 =−7 + 3 5 + 3 5 − 5 + 5 35 3 − 2 3 𝑥 = − 32 5 − 32 5 − 2 3 − 2 3 − 32 5 ÷− 2 3 − 32 5 ∙− 3 2 96 10 48 5 𝑥 = = = =

7) −0.6 𝑥+2.4 =8.4 −0.6 𝑥+2.4 =8.4 −0.6 𝑥+2.4 =8.4 −0.6 −0.6 −0.6𝑥 −1.44 8.4 = +1.44 +1.44 𝑥+2.4 = −14 −2.4 −2.4 −0.6𝑥 = 9.84 −0.6 −0.6 𝑥 = −16.4 𝑥 = −16.4 1 6 . 4 . 2 0 6 . 9 8 4 8 4 2 . 4 − 6 × 0 . 6 3 − 3 6 1 4 . 4 2

8) −3 𝑥+ 2 5 =3.6 − 6 5 18 5 36 10 −3𝑥 = + 6 5 + 6 5 24 5 −3𝑥 = −3 −3 24 5 ÷− 3 1 24 5 ∙− 1 3 − 24 15 − 8 5 𝑥 = = = =

6th Grade Solving: 7th Grade Solving: 8th Grade Solving: Equations of the form x + p = q  and  px = q  where  p, q and x are all nonnegative rational numbers. 7th Grade Solving: Equations of the form  px + q = r  and  p(x + q) = r where p, q, and r are specific rational numbers. 8th Grade Solving: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

9) 1 4 𝑥 2 + 5 3 − 7 8 𝑥− 13 20 =− 9 10 − 7 8 𝑥− 13 20 =− 9 10 1𝑥 8 1 8 𝑥 15 12 5 4 + − 3 4 𝑥 −6 8 𝑥 + 6 10 + 12 20 − 9 10 = − 6 10 − 6 10 − 3 4 𝑥 − 3 2 − 15 10 = − 3 2 − 4 3 − 3 4 12 6 𝑥 = ÷ ∙ = = 2 − 3 4 − 1 2