Can you please explain the steps I need to take so I can figure out the answer myself, so that I can better understand problems like this in the future. Thanks! What is the absolute value of x-y, if x is less than y? If they were numbers, I could figure this out, but I don’t know […]
Written on Saturday, March 8th, 2008 by frednoble :: 0 comments to this post
Can you please explain the steps I need to take so I can figure out the answer myself, so that I can better understand problems like this in the future. Thanks!
What is the absolute value of x-y, if x is less than y?
If they were numbers, I could figure this out, but I don’t know what to do here….!
Thanks for your help!
_____________________
The example in the book says;
find the absolute value of m-2, if m is less than 2.
if m is less than 2, then m-2 is less than 0, so
the absolute value of m-2 equals -(m-2), which equals -m+2 or 2-m
what?!
equals -m+2
(the negative is cut off above, because the m went to the next line, while the - stayed above, so just to avoid confusion I rewrote the first expression of the answer)
Yes, that did help, thanks!
Like the example in the book says:
if m is less than 2, then the absolute value of m-2 is -(m-2).
What does this mean?
If we use numbers instead of m-2, this should be more clear.
I bet you know that the absolute value of 5 is 5, while the absolute value of -5 is 5, right?
So, the absolute value of a positive number (or zero, actually) is itself. But, the absolute value of a negative number is not itself. So what is it? It’s 5 if the number is -5. But what is 5 relative to -5? It’s negative five without the negative, sure. But how do you relate the value of 5 relative to -5? It is actually the “negative of” negative five. Remember that the negative of a negative number is positive. So, the absolute value of -7 for example is -(-7) or +7. That is why, the absolute value of a negative number is its negative.
So to answer your question, since x is less than y, then x-y is a negative number. This means that the absolute value of x-y must be -(x-y) or simply y-x. Note that if x is greater than or equal to y, then the absolute value of x-y is simply x-y or itself.
Hope this helps.
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