1. Algebra 1
Section 2.1

2. Variables and Algebraic Expressions
62p is equivalent to 62 times p
If symbols are written next to each other with no operational sign between them, multiply them.

3. Definitions
Variable: a symbol used to represent any element of a given set of numbers
The set of numbers is called the domain of the variable.

4. Definitions Constant: a fixed number
Algebraic expression: a mathematical expression containing numbers, variables, and operational signs

5. Definitions
To evaluate an algebraic expression means to substitute values for the variable or variables and to simplify the result

6. Example 1 Evaluate: If x = -5, then x + 9 = -5 + 9
= 4
= 9½
= 11
= 12

7. Definitions The domain is the set of numbers used for the variable.
The corresponding set of values is called the range.

8. Example 1
The domain is {-5, ½, 2, 3}.
The range is {4, 9½, 11, 12}.

9. Example 2 Evaluate: If c = 5, then 10c = 10(5)
= 50
= 100
= 150

10. Example 2 c is the cost of one pencil. 10c is the cost of ten pencils.
If one pencil is 5 cents, ten pencils are 50 cents (50¢).
If one pencil is 15 cents, ten pencils are 150 cents ($1.50).

11. Words to Look For
The ability to translate phrases into algebraic expressions is foundational to success in algebra!

12. Example 3 a. the sum of a number and four n + 4
b. the difference between a number and five
n – 5

13. Example 3 c. one-third of a number n 3 1 n or
d. a number divided by six
or n ÷ 6 n 6

14. Example 3 e. the sum of three and eight times a number 3 + 8x
f. eight less than three times a number
3n – 8

15. Example 3
g. the quotient of the difference of a number and eight, and twice the number
n – 8 2n

16. Example 3 h. the opposite of the reciprocal of the square of a number1 s² -

17. Consecutive Integers n = the first integer n + 1 = the second integer
n + 2 = the third integer

18. Consecutive Even Integers
n = the first even integer
n + 2 = the second even integer
n + 4 = the third even integer

19. Consecutive Odd Integers
n = the first odd integer
n + 2 = the second odd integer
n + 4 = the third odd integer

20. Supplementary Angles
Two angles are supplementary if the sum of their angle measures is 180°.
If one angle is a degrees, then the other is (180 – a) degrees.

21. Complementary Angles
Two angles are complementary if the sum of their angle measures is 90°.
If one angle is a degrees, then the other is (90 – a) degrees.

22. Homework: pp