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# JRA Algebra Basics

### Algebra II Chapter 1 Equations + Inequalities

Question | Answer |
---|---|

Symbols, usually letters, used to represent unknown quantities. | variables |

Expressions that contain at least one variable. | algebraic expression |

1. Evaluate expressions inside grouping symbols. 2. Evaluate all powers. 3. Multiply and/or divide from left to right. 4. Add and/or subtract from left to right. | order of operations |

An algebraic expression that is a number, a variable, or the product of a number and one or more variable(s). | monomial |

Monomials that contain no variables. | constants |

The numerical factor of a monomial. | coefficient |

The sum of the exponents of a monomial's variables. | degree |

An expression of the form x multiplied n times. | power |

A monomial or a sum of monomials. | polynomial |

The monomials that make up a polynomial. | terms |

Two or more terms of a polynomial that can be combined. | like terms |

A polynomial with three unlike terms. | trinomial |

A polynomial with two unlike terms. | binomial |

A mathematical sentence that expresses the relationship between certain quantities. | formula |

The numbers that you use in everyday life. | real numbers |

A real number that can be written as a fraction. | rational number |

A real number that cannot be written as a fraction. | irrational number |

The rational numbers that you use for counting beginning with 1. | natural (counting) numbers |

All rational numbers beginning with 0 that do not have any decimals. | whole numbers |

All the rational numbers without decimals (includes negative numbers). | integers |

a+b = b+a or a(b) = b(a) | commutative property |

(a+b)+c = a+(b+c) or (ab)c = a(bc) | associative property |

a+0 = a = 0+a or a(1) = 1(a) | identity property |

a+(-a) = 0 = (-a)+a or if a does not equal 0, then a(1/a) = 1 - 1/a(a) | inverse property |

a(b+c) = ab+bc and (b+c)a = ba+ca | distributive property |

A mathematical sentence containing one or more variables. | open sentence |

A mathematical sentence stating that two mathematical expressions are equal. | equation |

Each replacement in an open sentence that results in a true sentence. | solution |

a = a | reflexive property |

If a = b, then b = a. | symmetric property |

If a = b, and b = c, then a = c. | transitive property |

If a = b, then a may be replaced by b and b may be replaced by a. | substitution property |

A number's distance from 0 on the number line. | absolute value |

The solution set for an absolute value equation that is not true. | empty set |

The property that states for any two real number, a and b, a < b, a = b, and a > b. | Trichotomy Property |

A solution set of an inequality which is read as "the set of all numbers x such that x is >, <, or = to y. | set-builder notation |

An inequality that consists of two inequalities joined by the word and or the word or. | compound inequality |

The graph of a compound inequality containing and. | intersection |

Compound inequalities involving the word and. | conjunctions |

Compound inequalities involving the word or. | disjunctions |

The graph of a compound inequality containing or. | union |

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LOSBH47