# Properties of Negation and Equality

Let a, b, and c be real numbers, variables, or algebraic expressions

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Property | Example |
---|---|

(-1)a = -a | (-1)7 = -7 |

-(-a) = a | -(-6) = 6 |

(-a)b = -(ab) = a(-b) | (-5)3 = -(5 * 3) = 5(-3) |

(-a)(-b) = ab | (-2)(-x) = 2x |

-(a + b) = (-a) + (-b) | -(x + 8) = (-x) + (-8) = -x - 8 |

if a = b, then a + c = b + c | 1/2 + 3 = 0.5 + 3 |

if a = b, then ac = bc | 4^2(2) = 16(2) |

if a +/- c = b +/- c, then a = b | 1.4 - 1 = 7/5 - 1 -> 1.4 = 7/5 |

if ac = bc and c /= 0, then a = b | 3x = 3 * 4 -> x = 4 |