Algebra 1 Section 2.1

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.

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.

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

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

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

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

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

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

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).

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

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

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

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

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

Example 3 h. the opposite of the reciprocal of the square of a number 1 s² -

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

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

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

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.

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.

Homework: pp. 48-50