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**Question 7: Complete the following table:**

** **

+ | âˆ’6 | âˆ’4 | âˆ’2 | 0 | 2 | 4 | 6 |

6 | | | | | | 10 | |

4 | | | | | | | |

2 | | | | | | | 8 |

0 | âˆ’6 | | | | | | |

âˆ’2 | | | | | | | |

âˆ’4 | | | | | | 0 | |

âˆ’6 | | | | âˆ’6 | | | |

**From the above table****(i) **Write all the pairs of integers whose sum is 0.

(ii) is (âˆ’4) + (âˆ’2) = (âˆ’2) + (âˆ’4)?

(iii) is 0 + (âˆ’6) = âˆ’6?

**ANSWER:**

(i) (6, âˆ’6), (4, âˆ’4), (2, âˆ’2), (0, 0), (âˆ’2, 2), (âˆ’4, 4) and (âˆ’6,6).

(ii) (âˆ’4) + (âˆ’2) = âˆ’6 = (âˆ’2) + (âˆ’4); Yes

(iii) 0 + (âˆ’6) = âˆ’6; Yes

+ | âˆ’6 | âˆ’4 | âˆ’2 | 0 | 2 | 4 | 6 |

6 | 0 | 2 | 4 | 6 | 8 | 10 | 12 |

4 | âˆ’2 | 0 | 2 | 4 | 6 | 8 | 10 |

2 | âˆ’4 | âˆ’2 | 0 | 2 | 4 | 6 | 8 |

0 | âˆ’6 | âˆ’4 | âˆ’2 | 0 | 2 | 4 | 6 |

âˆ’2 | âˆ’8 | âˆ’6 | âˆ’4 | âˆ’2 | 0 | 2 | 4 |

âˆ’4 | âˆ’10 | âˆ’8 | âˆ’6 | âˆ’4 | âˆ’2 | 0 | 2 |

âˆ’6 | âˆ’12 | âˆ’10 | âˆ’8 | âˆ’6 | âˆ’4 | âˆ’2 | 0 |

**Find an integer x such that(i) x + 1 = 0(ii) x + 5 = 0(iii) âˆ’3 + x = 0(iv) x + (âˆ’8) = 0(v) 7 + x = 0(vi) x + 0 = 0**

(i) x + 1 = 0 â‡’ x = âˆ’1

(ii) x + 5 = 0 â‡’ x = âˆ’5

(iii) âˆ’3 + x = 0 â‡’ x = 3

(iv) x + (âˆ’8) = 0 â‡’ x = 8

(v) 7 + x = 0 â‡’ x = âˆ’7

(vi) x + 0 = 0 â‡’ x = 0