Unit 6: Algebraic Representations and Applications

1. Unit 6: Algebraic Representations and Applications • Variable: a symbol, usually a letter, used to represent an unknown value.EX. x, y, n, etc. • Expression: a mathematical representation consisting of symbols, operators, and/or • variables to indicate operations to be performed on a group of numbers according to • the order of operations. Examples: 3(6) + 4x or -12 – 3 or -7h or lwh etc… • Equation: a mathematical sentence composed of algebraic expressions set equal to • each other. -7h = 14 or 3(6) + 4x = 26 or -5 + (13)(-2) = -31 etc… • Equal: having the same value. Ex. 5 = 4 + 1 or -2(-10) = -4(-5) etc… • Solving an equation: process (act) of finding the value of a variable that makes an • equation true. Example: 3y – 2 = 10 check the solution: 3y -2 = 10 • 3y -2 + 2 = 10 + 2 3(4) – 2 ? 10 • 3y = 12 12 – 2 ? 10 • 3y/3 = 12/3 10 = 10 • y = 4 YES IT CHECKS! • Solution: a value of the variable that makes the equation true. Ex. From previous ex. Y = 4 • Representations: concrete models, tables, graphs, verbal descriptions, and algebraic • generalizations of data.