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# Module 8 - Comp Ineq

### Compound Inequalities

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

If A = {x | x is an odd integer}, B = {x | x is an even integer}, C = {2,3,4,5}, and D = {18,19,20,21} list the element(s) of the following set. C ∪ D | Begin by listing the elements in set C. Then list the elements in set D. To find the union of the set C and set D, find the elements that are common to either one or the other set, or two both sets. C ∪ D = {2,3,4,5,18,19,20,21} |

If A = {x | x is an even integer}, B = {x | x is an odd integer}, C = {2,3,4,5}, and D = {22,23,24,25} list the element(s) of the following set. A ∩ D | Begin by listing the elements in set A. Then list the elements in set D. To find the intersection of set A and set D, find the elements that are common to both sets. A ∩ D = {22,24} |

If A = {x | x is an odd integer}, B = {x | x is an even integer}, C = {2,3,4,5}, and D = {2,3,4,5} list the element(s) of the following set. A ∩ D | A ∩ D = {3,5} |

Solve the compound inequality. x < 6 and x > -4 | First, find the interval for the inequality x < 6. Next, find the interval for the inequality x > -4. Note that the inequality uses the word "and." Find the set of points which satisfies both inequalities. (-4,6) |

Solve the compound inequality. x ≤ 1 and x ≥ 2 | There is no solution. ∅ |

Solve the compound inequality. x < -1 and x <1 | (-∞,-1) |

Solve the following compound inequality. Write the solution set in interval notation. x + 11 ≥ 3 and 7x - 12 ≥ 2 | x + 11 ≥ 3 and 7x - 12 ≥ 2 x ≥ 3 - 11 and 7x ≥ 2 + 12 x ≥ -8 and x ≥ (2 + 12)/7 x ≥ 2 Graph the solutions to the above inequalities. The solution set to x + 11 ≥ 3 and 7x - 12 ≥ 2 in interval notation is [2,∞). |

Solve the following compound inequality. Write the solution set in interval notation. x + 10 ≥ 7 and 6x - 4 ≥ 2 | The solution set in interval notation is [1,∞) |

Solve the compound inequality. 10 < x - 9 < 21 | 10 < x - 9 < 21 - This is the original compound inequality. 10 + 9 < x - 9 + 9 < 21 + 9 -Add 9 to all three parts. 19 < x < 30 - Simplify. The solution set in compact form is 19 < x < 30. Thus, the solution set in interval notation is (19,30). |

Solve the compound inequality. Write the solution in interval notation. x ≤ -5 or x ≥ 6 | The solution set to x ≤ -5 in interval notation is (-∞,-5]. The solution set to x ≥ 6 in interval notation is [6,∞) Thus, the solution set in interval notation is (-∞,-5] ∪ [6,∞) |

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gault_timothy