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# Algebra II Unit One

### Dr. Pittman's 1st Semester Course

Term | Definition |
---|---|

Reflexive Property of Equality | The property that a = a. One of the equivalence properties of equality |

Symmetric Property of Equality | Definition: If a = b, then b = a. Example of the Symmetric Property of Equality Equation 1: 5x + 20 = 35 Equation 2: 35 = 5x + 20 In spite of the rearranged terms, Equation 1 and Equation 2 are identical. |

Transitive Property of Equality | If a = b and b = c, then a = c. One of the equivalence properties of equality. Note: This is a property of equality and inequalities. One must be cautious, however, when attempting to develop arguments using the transitive property in other settings. |

Substitution Property of Equality | The substitution property of equality that, if a = b, then b can be substituted for a in any equation without changing the truth value of the equation. For example: •Let a = b. •Let d = a + 2. •Then d = b + 2. |

Variable | A symbol for a number we don't know yet. It is usually a letter like x or y. Example: in x + 2 = 6, x is the variable |

Constant | A fixed value. Example: in 2 + 6 = 8, 2, 6, and 8 are constants. Sometimes an a, b, or c can also be a constant. |

Numerical Expression | A numerical expression is a combination of numbers and one or more operation symbols. Example: 23 + 15 – 8 or 2x -6 |

Variable Expression | A variable is a symbol used to represent a number in an expression or an equation. The value of this number can change. An algebraic expression is a mathematical expression that consists of variables, numbers and operations. The value of this expression c |

Evaluate | To calculate the value of a word problem or a equation. |

Solution | Any and all value(s) of the variable(s) that satisfies an equation, inequality, system of equations, or system of inequalities. |

Properties of Equality | Properties and algebra rules for manipulating equations. Operations Addition: If a=b then a+c=b+c.Subtraction: If a=b then a–c=b–c. Multiplication: If a=b then ac=bc. Division: If a=b and c≠0 then a/c=b/c. Reflexive Property a=a Symmetric Property If a=b |

Distributive Property | |

Proof | |

Identity | An equation which is true regardless of what values are substituted for any variables. Identities: 1 + 1 = 2 (x + y)2 = x2 + 2xy + y2 a^2 ≥ 0 sin2 θ + cos2 θ = 1 |

Addition Property of Equality | |

Multiplication Property of Equality | |

Division Property of Equality | |

Extraneous Solution | |

No Solution | |

Literal Equation | |

Commutative Property of Addition | |

Commutative Property of Multiplication | |

Inverse Operations | Operations that undo each other: Ex. 1+5=6 or 5+1=6, additive 6-5=1 or 6-1=5, subtractive a/a= 1, multiplicative |

Absolute Value Equation | |

Inequality Equations |

Created by:
vickersm