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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
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
Homework Questions?
Section 3-4
Using Equations to Solve Problems
Objective
I want to be able to use the five-step plan to solve word problems.
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.
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.
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.
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
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.
Example 1 Continued
Step 5:
45 + 7 ( 12 ) = 129
45 + 84 = 129
129 = 129
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.
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
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
Section 3-5
Equations with the Variable on Both Sides
Objective
I want to be able to solve equations with the variable on both sides.
Example 1
Solve. 20+7x = 9x
Example 2
Solve. 4t = 50-6t
Example 3
Solve. 3 8x = 4 - x
5 5
Example 4
Solve. 4 r - 9 +2 =12r +14
Example 5
Solve. 3 x +2 - x = 2 x +1
Example 6
Solve. 2 3y +5 +9 = 6 y +3 +1
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.
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
Algebra Activity
Solving Equations (Variables on Both Sides of the Equal Sign)
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.
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
Clear your calculators!
Take out your agendas!
Copy down DUE DATES!
Homework:
Sections
3.4, 3.5
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)