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# Module 8

### Compound Inequalities

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

When solving exercises with inequalities, what are the three forms that a solution set can be expressed? | 1. Symbolic 2. Graphical 3. Interval Notation |

x ≤ 4 is an example of... | ...a Symbolic Solution |

(-∞,4] is an example of... | ...an Interval Notation |

Solve the inequality: 2x + 3 ≤ 11 | 2x + 3 ≤ 11 ........-3....-3 2x ≤ 8 |

How many solutions does 2x ≤ 8 have? | Infinite |

The solution of: -4m>-20 equals... | m<5 |

The solution set of a compound inequality formed by the word "and" is the... | ...intersection of the solution sets of the two inequalities |

Intersection of Two Sets | The set of all elements common to both sets |

Solve: x-7<2 and 2x+1<9 | x-7<2 and 2x+1<9 ..+7+7............-1..-1 x<9 and 2x<8 x<9 and x<4 |

Find solution set of: x<9 and x<4 | (-∞,4) |

The solution set of a compound inequality formed by the word "or" is... | ...the union of the solution sets of the two inequalities |

The union of two sets... | is the set of elements that belong to either (one, or the other, or both) of the sets |

Notation a ≥ b means that | a is greater than or equal to b (or, equivalently, not less than b) |

The notation a ≤ b means that | a is less than or equal to b (or, equivalently, not greater than b) |

The notation a < b means that | a is less than b. |

The notation a > b means that | a is greater than b |

Solve 5x-3≤10 or x+1≥5 | 5x-3≤10 or x+1≥5 .....+3 +3........-1-1 5x≤13 x≥4 /5 /5 x≤13/5 x≥4 |

Find the solution set for x≤13/5 x≥4 Write in Interval Notation | Solution Set: (-∞13/5]U[4,∞) |

If all real numbers, solution set is what? | Solution Set: (-∞,∞) |

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