If a, b, and c are real numbers, which of the following arenecessarily true? 1.

Question

If a, b, and c are real numbers, which of the following arenecessarily true? 1. If a , b and ab doesn't equal 0 then 1/a >1/b 2. If a < b, then ac < bc for all c 3. If a< b, then a + c < b + c for all c 4. If a < b, then -a > -b Please provide explanation. Thanks If a, b, and c are real numbers, which of the following arenecessarily true? 1. If a , b and ab doesn't equal 0 then 1/a >1/b 2. If a < b, then ac < bc for all c 3. If a< b, then a + c < b + c for all c 4. If a < b, then -a > -b Please provide explanation. Thanks

Explanation / Answer

If a, b, and c are real numbers, which of the following arenecessarily true? 1. If a , b and ab doesn't equal 0 then 1/a >1/b That is not necessarily true, contraexample b=1 and a=-1 1/-1 < 1/1 -1<1 2. If a < b, then ac < bc for all c That is not necessarily true, contraexample if c<0 a<b => 2<5     Letc=-1 ac>bc => -2>-5 3. If a< b, then a + c < b + c for all c This is true If a<b then b-a>0 propertie of the real numbers 4. If a < b, then -a > -b This is true propertie of the real numbers propertie of the real numbers

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