Kosta: If b>c and |a-b|>|a-c| then b>a 2/.

[kosta]

Help me resolve that inequalities . To prove that:

If b>c and |a-b|>|a-c| then

b>a

2/.

If b>c and b>a then |a-b|>|a-c|

Thank you.
Kosta

 

[Deleted member 4993]

Help me resolve that inequalities .To prove that:
if b>c and |a-b|>|a-c| then

b>a

2/. if b>c and b>a then |a-b|>|a-c|

What are your thoughts?

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[stapel]

Help me resolve that inequalities . To prove that:

If b>c and |a-b|>|a-c| then

b>a

2/.

If b>c and b>a then |a-b|>|a-c|

Are these two separate exercises? If so, do you mean the following?

. . . . .\(\displaystyle \mbox{1. If }\, b\, >\, c\, \mbox{ and }\, \bigg|\, a\, -\, b\, \bigg|\, >\, \bigg|\, a\, -\, c\, \bigg|,\, \mbox{ then }\, b\, >\, a.\)

. . . . .\(\displaystyle \mbox{2. If }\, b\, >\, c\, \mbox{ and }\, b\, >\, a,\, \mbox{ then }\, \bigg|\, a\, -\, b\, \bigg|\, >\, \bigg|\, a\, -\, c\, \bigg|.\)

(In the above, I'm assuming that the floating "2/." has no particular meaning.)

Please provide correction or confirmation of the above. When you reply, please provide a clear listing of your thoughts and efforts so far. Thank you!