1. Exercise
Define inverse operations.
operations that undo each other

2. Exercise Name two pairs of inverse operations. Addition/subtraction
Multiplication/division

3. Exercise Explain the difference between an expression and an equation.
Equations have two sides separated by an equal sign, while an expression represents a single number.

4. Exercise
Solve x + 7 = −16
x = −23

5. Exercise
Solve 9 = y − 3
y = 12

6. Multiplication Property of Equality
For all integers a, b, and c, if a = b, then ac = bc.

7. Example 1
Solve = 14
x −4
x = −56

8. Example 2
Solve 9y = 72
y = 8

9. Example 3
Solve −n = 37
n = −37

10. Example 4
Write each word phrase as a mathematical expression. Use n for the variable.
a. twice a number 2n
b. four times a number 4n
c. one-third of a number
or n
1 3
n 3

11. Example 4
Write each word phrase as a mathematical expression. Use n for the variable.
d. quotient of a number and eight
or n
1 8
n 8
e. quotient of eight and a number
8 n

12. Example 5
Write an algebraic expression for the ages of Jon and Eileen. Jon’s age is twice Joyce’s, and Eileen’s age is one-fourth of Joyce’s.
Let x = Joyce’s age.
Jon’s age is 2x.
Eileen’s age is x or .
1 4
x 4

13. Example 6
Write an equation for the sentence “Nineteen dollars is the result of dividing the cost of a tennis racket by three.”
= 19
c 3

14. Example 7
The advertised cost for three items is $69. What is the unit price?
Read the sentence carefully. Choose a variable for the unknown.
Let x = price per unit

15. Example 7
The advertised cost for three items is $69. What is the unit price?
The verb is indicates the equal sign.
3x =

16. Example 7
The advertised cost for three items is $69. What is the unit price?
Place 69 to the right of the equal sign.
Divide both sides of the equation by 3.
x = 23

17. Example
Name the inverse operation, including the quantity, that would be used to solve each equation.

18. Example
9n = 36

19. Example
x −4
= 12

20. Example
6x + x = −56

21. Example
Solve.

22. Example
z 2
= 14

23. Example
3n = −51

24. Example
−4m = −6(8)

25. Example
z −8
= −3

26. Example
7 − c = 32

27. Example
(13 − 4)x = 108

28. Example
−1(13x) = −42 + 3

29. Exercise
Write an equation and solve: Eighty increased by the sum of three times a number and nine is one hundred ten.

30. Exercise
On a 627 mi. trip, Mr. Johannson traveled by airplane, automobile, and bicycle. He traveled seven times farther by plane than by car and one-seventh as far by bicycle as by car.

31. Exercise
Write the following sum as a single fraction: 2n +
n 3

32. Exercise For what values of the variable or variables would
(a) be negative
and (b) be positive?
5 x
y z