Chapter 1 Section 1 Algebraic Expressions, Real Numbers, and Interval Notation

Vocabulary Variables – letters that represent various numbers Constant – represents only one number Algebraic Expression – combination of variables and numbers using math operations.

Algebraic Expression Algebraic Expression: x + 6 3x + 5

English Words for the Basic Operations Addition Sum Plus Increased by More than Subtraction Difference Minus Decreased by Less than

English Words for the Basic Operations Multiplication Product Times Twice Of Division Quotient Divide Divide by

Evaluate Algebraic Expressions a) If x = 5, evaluate: 8 + 6x b) If x = 9, evaluate:

Order of Operations Parentheses – fractions Exponents Multiplication, Division from LEFT to RIGHT Addition, Subtraction from LEFT to RIGHT

Try 4 + 3 • 2 18 – 2 + 3 2 • 32 - 12

Simplify 1a) 16 ÷ 4 • 2 – 16 ÷ 8 2a) 8 – 2 • 3 - 4

Answers 1a) 6 2a) - 2

Number systems Real Imaginary Natural - Counting Whole { 0, 1, 2, . . .} Integers { . . . -1, 0 , 1, . . .} Rational { fractions} Irrational Imaginary

Symbol Is an element of: Is not an element of:

Example

True/False -5 < -3 -9 ≥ 6 3

Answers True False

Number line Origin Positive, negative Graph – on the line

Set Notation Interval Set builder Roster Infinite, finite sets [a, b], (a, b] {x | x > 4 } {5, 6, 7, 8, . . . }

Express in set-builder notation (1, 6] [- 4, 3] (3, )

Answers {x| -1< x ≤ 6} {x | - 4 ≤ x ≤ 3} {x| x > 3 }

Graph the following ( -1, 4] {x | -1 < x ≤ 4 } (- 4, )