![Page 1: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/1.jpg)
Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus twice a number 4.) six less than a number Simplify.
1.)3 + 2x - 2x 2.)2 4t +6 - 4t
2 23.)55 - 2w + 2w 4.) s +5 - s
5 5
5.)8 +5 x -1 - x 6.)- 333u+ 22 +333u
![Page 2: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/2.jpg)
Did you get these answers? Translate each phrase into a variable expression. Let n stand for the number.
1.) five times a number 5n
2.) one third of a number ( 1/3 )n
3.) eight minus twice a number 8 – 2n
4.) six less than a number n - 6
Simplify.
1.) 3 + 2x - 2x = 3 2.) 2 4t + 6 - 4t = 4t +12
2 23.) 55 - 2w + 2w = 55 4.) s + 5 - s = 5
5 5
5.) 8 + 5 x -1 - x = 4x + 3 6.) - 333u + 22 + 333u = 22
![Page 3: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/3.jpg)
Homework Questions?
![Page 4: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/4.jpg)
Section 3-4
Using Equations to Solve Problems
![Page 5: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/5.jpg)
Objective
I want to be able to use the five-step plan to solve word problems.
![Page 6: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/6.jpg)
Plan for Solving a Word Problem
Step 1 – Read the problem carefully. Decide what unknown numbers are asked for and what facts are known. Making a sketch may help.
Step 2 – Choose a variable and use it with the given facts to represent the unknowns described in the problem.
![Page 7: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/7.jpg)
Plan for Solving a Word Problem
Step 3 – Reread the problem and write an equation that represents relationships among the numbers in the problem.
Step 4 – Solve the equation and find the unknowns asked for.
Step 5 – Check your results with the words of the problem. Give the answer.
![Page 8: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/8.jpg)
Example 1 Sarah already has 45 stamps in her
collection, and she gets 7 new stamps each month. How long will it take before she has 129 stamps in her collection?
Step 1: The problem asks for the time it will take to get 129 stamps.
![Page 9: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/9.jpg)
Example 1 continued
Step 2:
Let m = the number of months it will take.
Step 3:
Future stamps = current stamps plus 7 more each month
129 = 45 + 7m
![Page 10: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/10.jpg)
Example 1 Continued
Step 4:
129 = 45 + 7m
-45 -45
84 = 7m
12 = m
It will take Sarah 12 months to have 129 stamps in her collection.
![Page 11: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/11.jpg)
Example 1 Continued
Step 5:
45 + 7 ( 12 ) = 129
45 + 84 = 129
129 = 129
![Page 12: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/12.jpg)
Example 2
The length of a rectangle is 3 inches more than the width. Find the length and width if the perimeter of the rectangle is 98 inches.
Step 1: the problems asks for the length and width of the rectangle.
![Page 13: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/13.jpg)
Example 2 Continued
Step 2: Let w = the width of the rectangle. Then w + 3 = the length of the rectangle.
Step 3: Use the formula P = 2l + 2w
Step 4:
98 = 2(w + 3) + 2w
98 = 2w + 6 + 2w
98 = 4w + 6
92 = 4 w
23 = w
![Page 14: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/14.jpg)
Example 2 Continued
Step 5:
The length of the rectangle is 26 in. and the width is 23 in.
2 ( 26) + 2 ( 23 ) = 52 + 46 = 98
![Page 15: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/15.jpg)
Section 3-5
Equations with the Variable on Both Sides
![Page 16: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/16.jpg)
Objective
I want to be able to solve equations with the variable on both sides.
![Page 17: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/17.jpg)
Example 1
Solve. 20+7x = 9x
![Page 18: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/18.jpg)
Example 2
Solve. 4t = 50-6t
![Page 19: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/19.jpg)
Example 3
Solve. 3 8x = 4 - x
5 5
![Page 20: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/20.jpg)
Example 4
Solve. 4 r - 9 +2 =12r +14
![Page 21: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/21.jpg)
Example 5
Solve. 3 x +2 - x = 2 x +1
![Page 22: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/22.jpg)
Example 6
Solve. 2 3y +5 +9 = 6 y +3 +1
![Page 23: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/23.jpg)
Try These! Solve each problem using the five-step plan. 1.) Six less than five times a number is 74.
Find the number. 2.) Eight less than one half a number is -44.
Find the number. 3.) Tom has read 143 pages of the 251 pages
in a book. If he reads 12 pages a day, how long will it take him to finish the book?
4.) The longest side of a triangle is 3 more
than twice the shortest side and the remaining side is 2.4 cm. Find the lengths if the perimeter is 12 cm.
![Page 24: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/24.jpg)
Try These! Solve each problem using the five-step plan. 1.) Six less than five times a number is 74. Find
the number. 16 2.) Eight less than one half a number is -44. Find
the number. - 72 3.) Tom has read 143 pages of the 251 pages in a
book. If he reads 12 pages a day, how long will it take him to finish the book? 9 days
4.) The longest side of a triangle is 3 more than
twice the shortest side and the remaining side is 2.4 cm. Find the lengths if the perimeter is 12 cm. 2.4, 2.2, 7.4 cm
![Page 25: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/25.jpg)
Algebra Activity
Solving Equations (Variables on Both Sides of the Equal Sign)
![Page 26: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/26.jpg)
And These!
1.) 9x = 2x + 21 4. ) 3 k - 8 = k + 4
x +102.) 4t = 60 - 8t 5 .) = 2x
3
2x - 73.) 2w = 42 +9w 6.) = 3x
2
7.) Find a number whose product wit h 10 is the same
as its sum with 45.
![Page 27: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/27.jpg)
And These!
1.) 9x = 2x + 21 4. ) 3 k - 8 = k + 4
x = 3 k = 14
x +102.) 4t = 60 - 8t 5 .) = 2x
3
t = 5 x = 2
2x - 73.) 2w = 42 +9w 6.) = 3x
2
7 w = - 6 x = -
4
7.) Find a number whose product with 10 is the same
as its sum with 45. 5
![Page 28: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/28.jpg)
Clear your calculators!
Take out your agendas!
Copy down DUE DATES!
Homework:
Sections
3.4, 3.5
![Page 29: Warm-Up...Sep 10, 2013 · Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus](https://reader035.vdocument.in/reader035/viewer/2022081601/60ef8531fb66807dda658a12/html5/thumbnails/29.jpg)
Journal Entry
TOPIC: Solving Equations
Answer the following question: Write the examples that had the empty set and identity as the solution. Explain what is meant by an empty set/null set and an identity. (Hint: look on pg. 117)