Chapter Three:  Equations

Take notes on the following topics.

Chapter Three

Section 3.1

Section 3.2

Section 3.3

Section 3.4

Section 3.5

Section 3.6

Section 3.7

Section 3.8

Section 3.9

Section 3.10

Section 3.11

Section 3.12

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Section 3.11     More Expressions and Equations

 Algebraic Representations of  Three Sets of Integers

Example # 1 (Consecutive Integers)

Find three consecutive integers with a sum of 108.

What are you to find? 3 consecutive integers What is given? The sum of the three integers is 108. Choose a variable. Let n = the 1st integer. Then n + 1 = the 2nd integer and   n + 2 = the 3rd integer Write an equation. The sum of the three integers is 108. first + second + third =108 n + (n + 1) + (n +2 ) =108 Solve the equation. n + (n + 1) + (n +2 ) =108      n + n + 1 + n + 2 = 108                       3n + 3 = 108                 3n + 3 - 3 = 108 - 3                             3n = 105                        (3n)/3 = 105/3                                n = 35                           n + 1 = 36                           n + 2 = 37 Check in the word of the original problem. Is the sum of the three consecutive integers 108? Yes, because 35 + 36 + 37 = 108 State the answer. The three consecutive integers are 35, 36, and 37.

Examples # 2 (Consecutive Even Integer)

Find three consecutive even integers with a sum of  -90.

What are you to find? three consecutive even integers What is given? The sum of the three consecutive even integers is -90. Choose a variable. Let n = the 1st even integer Then n + 2 = 2nd even integer and n + 4 = 3rd even integer Write an equation. The sum of the 3 cons. even integers is -90. first + second + third = -90 n + (n + 2) + (n + 4) = -90 Solve the equation. n + (n + 2) + (n + 4) = -90       n + n + 2 + n + 4 = -90                        3n + 6 = -90                  3n + 6 - 6 = -90 - 6                               3n = -96                          (3n)/3 = (-96)/3                                  n = -32                            n + 2 = -30                            n + 4 = -28 Check in the word of the original problem. Is the sum of the three consecutive integers -90? Yes, because -32 + (-30) + (-28) = -90 State the answer. The three consecutive integers are -32, -30, and -28.

Examples # 3 (Consecutive Odd Integer)

Find three consecutive odd integers with a sum of  135.

What are you to find? three consecutive odd integers What is given? The sum of the three consecutive odd integers is 135. Choose a variable. Let n = the 1st odd integer Then n + 2 = 2nd odd integer and n + 4 = 3rd odd integer Write an equation. The sum of the 3 cons. odd integers is 135. first + second + third = 135 n + (n + 2) + (n + 4) = 135 Solve the equation. n + (n + 2) + (n + 4) = 135       n + n + 2 + n + 4 = 135                        3n + 6 = 135                  3n + 6 - 6 = 135 - 6                               3n = 129                          (3n)/3 = (129)/3                                  n = 43                            n + 2 = 45                            n + 4 = 47 Check in the word of the original problem. Is the sum of the three consecutive integers 135? Yes, because -32 + (-30) + (-28) = 135 State the answer. The three consecutive integers are 43, 45, and 47.

(Examples provided by Prentice Hall)

Take class notes.

Before starting your homework, rework the examples that are illustrated in this section of your textbook and the examples that I demonstrated in class. 

Then do your homework.

Write down questions (examples or concept that you do not understand).......then.............. Ask these questions in class.