CHAPTER 3                            LESSON 3

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## Before we start the lesson, there will be a quiz next lesson on Evaluating Addition and Subtraction Expressions, Writing Addition and Subtraction Expressions, and Solving Addition and Subtraction Equations.  This quiz will be submitted to me for a grade.

An equation has three parts: a left side and a right side with an equal sign in between. A mathematical statement says that "the left side" is equal to, or the same as, "the right side." In solving an equation, your job is to find value(s) for the variable(s) that make the statement "the left side is equal to the right side" true.

Problem 1

Al Oerter won the Olympic Discus Throw four times.  His 1956 throw of 563.6 decimeters was 84.2 decimeters shorter than his 1968 throw.  How far did he throw the discus in 1968?

SOLUTION:

1.   Write an equation.

2.   What is happening in the equation? 84.2 is being subtracted from d.  So to undo the subtraction and get d by itself, we add 84.2 to both sides of the equation.

1956 distance                   1968 distance

563.6                =                d -  84.2

563.6 + 84.2                      =                d -  84.2 + 84.2         We add 84.2 to undo the subtraction

647.8                    =                     d

Al's 1968 throw was 647.8 decimeters

Problem 2

Solve  x + 27 = 45

x + 27 = 45               What is happening in the equation?  27 is being added.  So we
undo the addition by subtracting 27 from both sides of the equation.

x + 27 - 27 = 45 - 27

x   =   18

NOW YOU TRY J

Solve each equation

1.  k + 7 = 34

2.  y - 9 = 48

3.  61 = n -  4

4.  109 = n -17

5.  93 = q + 8

6.  216 = 63 + r

7.  56 = 11 + s

8.  193 = t - 81
9.   w + 806 = 909

10.  x  - 81 = 53

11.  117= z - 86

12.  231 = g + 12

13.  m + 51.2 = 86.1

14.  6.17  = 0.41 + p

15.  20.13 = a + 8.16

16.  r  - 2.96 = 1.32

17.  36.2 = x -0.8

18.  y -1.07 = 2

For each exercise, write and solve an equation.

19.  26 more than a number b is 47.

20.  19 less than a number d is 62.

21.  A number y increased by 34 is 112.

22.  A number n decreased by 68 is 17.

23. Mary Peters won the 1972 Olympic Women's Pentathlon with 4801 points. This was 56 points more than
the score of the 1976 winner, Sigrun Siegl. How many points did Sigrun Siegl earn ?

24. Robert Mathias won the Olympic Decathlon in 1948 and 1952. His 1948 score of 7139 points was 748
points less than his 1952 score. How many points did he score in 1952?

25. Al Oerter's 1960 discus throw was 56 decimeters shorter than his 1968 throw. His 1968 throw was 647.8

decimeters. How far did he throw the discus in 1960?

26. Oerter's 1964 discus throw was 46.4 decimeters longer than his 1956 throw. His 1956 throw was 563.6

decimeters. How far did he throw the discus in 1964?