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# Unit #5 Vocabulary

### Terrell-UNIT5:SOLVING EQUATIONS: Terms re: solving equations (4/06).

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

EXPRESSION | A symbol or combination of symbols that represent a mathematical quantity. NOTE: The symbols can be numbers or variables, and there are NO EQUAL SIGNS within an expression. | 2x + 3 |

LIKE TERMS | Terms that contain the same variables, with the corresponding (matching) variables having the same exponent. | 7x and 5x |

EQUATION | A mathematical sentence in which two expressions are set equal to each other. | 2x + 3 = 5 |

INVERSE | Opposite. | Addition and subtraction are inverses of each other. |

IDENTITY | An equation that is true for all real numbers. | 3x - 3 = 2x + (x - 3) is an identity, because it will simplify to the same expression on each side of the equation and work for all real numbers. |

ASSOCIATIVE PROPERTY | A property of real numbers that allows the changing of the grouping of addends or factors without changing the result. | For 2 + (3 + 5) = (2 + 3) + 5, both expressions have a sum of 10. |

DISTRIBUTIVE PROPERTY | A property of real numbers that allows each term of an expression inside a set of parentheses to be multiplied by each term of an expression outside of the parentheses without changing the result. | For 2(3 + 5) = 2 * 3 + 2 * 5, both expressions would equal 16. |

VARIABLE | A letter that represents a quantity or quantities. | x, y, t, n |

COEFFICIENT | The numerical factor of an algebraic term (i.e. the number multiplied by a variable). | For 3x, x is the variable, and 3 is the coefficient. |

ADDITIVE INVERSE PROPERTY | The sum of any number and its opposite is zero. | 2 + (-2) = 0; therefore, 2 and -2 are additive inverses. |

MULTIPLICATIVE INVERSE PROPERTY | The product of a number and its reciprocal is 1. | 5/3 * 3/5 = 1; therefore, 5/3 and 3/5 are multiplicative inverses. |

ADDITION PROPERTY OF EQUALITY | The property of real numbers which states that adding the same term to both sides of an equation will keep the each expression equivalent and the equation balanced. | For x + 2 = 3 - 4x, 4x can be added to both sides of the equation without changing the value of it. |

SUBTRACTION PROPERTY OF EQUALITY | The property of real numbers which states that subtracting the same term from both sides of an equation will keep the each expression equivalent and the equation balanced. | For x + 2 = 3 - 4x, x can be subtracted from both sides of the equation without changing the value of it. |

MULTIPLICATION PROPERTY OF EQUALITY | The property of real numbers which states that multiplying the same term on both sides of an equation will keep the each expression equivalent and the equation balanced. | For 3/5y = 10, 5/3 can be multiplied on each side of the equation without changing the value of it. |

DIVISION PROPERTY OF EQUALITY | The property of real numbers which states that dividing both sides of an equation by the same term will keep the each expression equivalent and the equation balanced. | For 35f = 105, 35 can be divided into each side of the equation without changing the value of it. |

INEQUALITY | A mathematical sentence that expresses the relationship between two expressions using the symbols <, >, (< or equal to), or (> or equal to). | 3x + 5 < -52 |

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