True or Not

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Cindy Burgess

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Apr 13, 2013
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1. I believe that this statement: a>b, and c is positive, then ac>bc is true 2. If a^2=b^2, then a=b I believe that this statement is true 3. If a > b, and c is positive, the a/c > b/c I believe that this is not true, but I can't think of a counterexample to prove it Please help
 
a does not equal b. however the absolute value of a equals absolute value of b. since a>b and a^2=b^2 then b has to be a negative number and a is the absolute value of b. plug in any negative number for b and plug in any absolute value of b for a and youll see that the inequality a/c>b/c.
 
stapel said:
Why? Please bear with me. I can't make my problems look like you do (spacing) and then showing them once I hit reply. This is why I believe the first problem a>b, and c is positive, then ac > bc If I use a=3 b=-3 c= 4 I get 3>-3 12 > -12 If I use a=3 b=2 c=5 Then I get 3 > 2 15>10 If I use a=3 b=2 c=1 then I get 3>2 3>2


Why? My 2nd problem a^2 = b^2 , then a=b a=3 b=-3 3^2 = -3^2 9=9 b would always have to be the negative of a


Why not?
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My 3rd problem a>b, and c is positive, then a/c > b/c If I use a=3 b= -3 c=4 I get 3/4 > -3/4 If I use a=3 b=2 c=5 I get 3/5 > 2/5 If I use a=3 b=2 c=1 Then I get 3/1 > 2/1 Are Are they all 3 true?
 
Cindy Burgess said:
My 3rd problem a>b, and c is positive, then a/c > b/c If I use a=3 b= -3 c=4 I get 3/4 > -3/4 If I use a=3 b=2 c=5 I get 3/5 > 2/5 If I use a=3 b=2 c=1 Then I get 3/1 > 2/1 Are Are they all 3 true?
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So you are asking if 3/4> -3/4? The number on the left is positive, the number on the right is negative! What does that tell you? If 3/5> 2/5? Is 3> 2? Is 3> 1?

If you honestly do not know how to tell, for specific numbers, which is larger then you really have no hope of being able to prove general statements about ">"! You need to talk to your teacher about this.

But certainly, to be able to prove this, you need to know, at least, that "If a> b and c> 0 then ac> bc" and "if a> b and c< 0 then ac< bc".
 
HallsofIvy said:
So you are asking if 3/4> -3/4? The number on the left is positive, the number on the right is negative! What does that tell you? If 3/5> 2/5? Is 3> 2? Is 3> 1?

If you honestly do not know how to tell, for specific numbers, which is larger then you really have no hope of being able to prove general statements about ">"! You need to talk to your teacher about this.

But certainly, to be able to prove this, you need to know, at least, that "If a> b and c> 0 then ac> bc" and "if a> b and c< 0 then ac< bc".
Click to expand...
No, I do know that 3/4 > -3/4 and that 3/5 > 2/5 and 3>2 and 3>1 What I am trying to prove is that it is True for all instances where c is positive and you just answered that for me--Thank you--I'm sorry if the way I worded it made me sound ignorant. Cindy
 
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