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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