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M4:LSN9 Writing and Solving Linear Equations Activating Prior Knowledge – Notes Transcribe the expression using mathematical symbols. 1. Four less than 2. Six more than three times a half a number number 3. Twelve more than three times a number 4. Twice as large as a number Tie to LO Learning Objective Today, we will apply and solve linear equations. CFU M4:L1 Writing Equations Using Symbols Skill Development/Guided Practice – Notes #1 1. A whole number has the property that when the number is added to five it is 4. What is the number? 𝒙+𝟓=𝟒 −𝟓 − 𝟓 𝒙 = −𝟏 The number is -1 Holt CA Course 2 CFU M4:L1 Writing Equations Using Symbols Skill Development/Guided Practice – Notes #2 2. Eight times the result of subtracting 3 from a number is equal to the number increased by 25. What is the number? 𝟖 𝒙 − 𝟑 = 𝒙 + 𝟐𝟓 𝟖𝒙 − 𝟐𝟒 = 𝒙 + 𝟐𝟓 −𝒙 −𝒙 𝟕𝒙 − 𝟐𝟒 = 𝟐𝟓 +𝟐𝟒 + 𝟐𝟒 ÷𝟕 ÷𝟕 𝟕𝒙 = 𝟒𝟗 𝒙=𝟕 Holt CA Course 2 The number is 7 CFU M4:L1 Writing Equations Using Symbols Skill Development/Guided Practice – Notes #3 3. Miriam read a book with an unknown number of pages. The first week she read 𝟏 five less than of the pages. The second week she read 171 pages and finished the 𝟑 book. Write an equation that represents the total number of pages in the book and find how many pages are in the book. 𝟏 𝒙 − 𝟓 + 𝟏𝟕𝟏 = 𝒙 𝟑 𝟏 𝒙 + 𝟏𝟔𝟔 = 𝒙 𝟑 𝟏 − 𝒙 𝟑 𝟏 − 𝒙 𝟑 𝟐 𝟏𝟔𝟔 = 𝒙 𝟑 CFU Holt CA Course 2 M4:L1 Writing Equations Using Symbols Skill Development/Guided Practice – Cont. Notes #3 3. Miriam read a book with an unknown number of pages. The first week she read 𝟏 five less than of the pages. The second week she read 171 pages and finished the 𝟑 book. Write an equation that represents the total number of pages in the book and find how many pages are in the book. 𝟐 𝟏𝟔𝟔 = 𝒙 𝟑 𝟐 ÷ 𝟑 𝟐 ÷ 𝟑 𝟑 𝟐 𝟑 𝟐 𝟏𝟔𝟔 = 𝟑 𝒙 𝟐 𝟐𝟒𝟗 = 𝒙 There are 249 pages in the book. CFU Holt CA Course 2 M4:L1 Writing Equations Using Symbols Concept Development Review – Pair Share How is the perimeter of a rectangle calculated? How is the area of a rectangle calculated? CFU Holt CA Course 2 M4:L1 Writing Equations Using Symbols Skill Development/Guided Practice – Notes #4 (HW#8) 4. The length of a rectangle is 4 more than 3 times the width. If the perimeter is 18.4 cm, what is the area of the rectangle. 𝒑𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓 = 𝟐 𝒍𝒆𝒏𝒈𝒕𝒉 + 𝟐(𝒘𝒊𝒅𝒕𝒉) 𝒂𝒓𝒆𝒂 = 𝒍𝒆𝒏𝒈𝒉𝒕𝒉 𝒙 𝒘𝒊𝒅𝒕𝒉 𝟐 𝟒 + 𝟑𝒙 + 𝟐𝒙 = 𝟏𝟖. 𝟒 𝟖 + 𝟔𝒙 + 𝟐𝒙 = 𝟏𝟖. 𝟒 𝟖 + 𝟖𝒙 = 𝟏𝟖. 𝟒 −𝟖 −𝟖 𝟖𝒙 = 𝟏𝟎. 𝟒 𝐈𝐬 𝐭𝐡𝐚𝐭 𝐨𝐮𝐫 𝐟𝐢𝐧𝐚𝐥 𝐚𝐧𝐬𝐰𝐞𝐫? Holt CA Course 2 ÷𝟖 ÷𝟖 𝒙 = 𝟏. 𝟑 CFU M4:L1 Writing Equations Using Symbols Skill Development/Guided Practice – cont. Notes #4 (HW#8) 4. The length of a rectangle is 4 more than 3 times the width. If the perimeter is 18.4 cm, what is the area of the rectangle. 𝒑𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓 = 𝟐 𝒍𝒆𝒏𝒈𝒉𝒕𝒉 + 𝟐(𝒘𝒊𝒅𝒕𝒉) 𝒂𝒓𝒆𝒂 = 𝒍𝒆𝒏𝒈𝒉𝒕𝒉 𝒙 𝒘𝒊𝒅𝒕𝒉 𝒙 = 𝟏. 𝟑𝒄𝒎 𝐰𝐡𝐢𝐜𝐡 𝐢𝐬 𝐭𝐡𝐞 𝐰𝐢𝐝𝐭𝐡 𝒍𝒆𝒏𝒈𝒕𝒉 = 𝟑𝒙 + 𝟒 𝒍𝒆𝒏𝒈𝒕𝒉 = 𝟑(𝟏. 𝟑) + 𝟒 𝒍𝒆𝒏𝒈𝒕𝒉 = 𝟕. 𝟗 𝒄𝒎 𝒂𝒓𝒆𝒂 = 𝒍𝒆𝒏𝒈𝒕𝒉 𝒙 𝒘𝒊𝒅𝒕𝒉 𝒂𝒓𝒆𝒂 = 𝟕. 𝟗(𝟏. 𝟑) 𝒂𝒓𝒆𝒂 = 𝟏𝟎. 𝟐𝟕 cm² Holt CA Course 2 CFU M4:L1 Writing Equations Using Symbols Skill Development/Guided Practice – Notes #5 The sum of three consecutive integers is 372. What are the numbers? 𝒙 + 𝒙 + 𝟏 + 𝒙 + 𝟐 = 𝟑𝟕𝟐 𝟑𝒙 + 𝟑 = 𝟑𝟕𝟐 −𝟑 −𝟑 𝟑𝒙 = 𝟑𝟔𝟗 𝐈𝐬 𝐭𝐡𝐚𝐭 𝐨𝐮𝐫 𝒙 = 𝟏𝟐𝟑 𝐟𝐢𝐧𝐚𝐥 𝐚𝐧𝐬𝐰𝐞𝐫? The numbers are 𝟏𝟐𝟑, 𝟏𝟐𝟑 + 𝟏, 𝟏𝟐𝟑 + 𝟐 𝟏𝟐𝟑, 𝟏𝟐𝟒, 𝟏𝟐𝟓 ÷𝟑 Holt CA Course 2 ÷𝟑 CFU M4:L1 Writing Equations Using Symbols Skill Development/Guided Practice – Notes #6 (HW #9) 6. Two hundred and fifty tickets are available for sale for a school dance. On Monday 35 tickets sold. An equal number of tickets were sold each day for the next 5 days. How many tickets were sold on those 5 days? 𝟐𝟓𝟎 = 𝟑𝟓 + 𝟓𝒙 −𝟑𝟓 − 𝟑𝟓 𝟐𝟏𝟓 = 𝟓𝒙 ÷𝟓 ÷𝟓 𝟒𝟑 = 𝒙 𝟒𝟑 tickets were sold on each of the 5 days. Holt CA Course 2 CFU Closure – 1. What did we learn today? 2. Why is this important to you? 3. How can you check if you have the correct solution to a linear equation. Homework Problem Set Page S.32 2 – 9 all CFU