Question 254575: Suppose a is a negative real number. Determine if the following is a positive or negative number:
a) –a b) │-a│ c) -│a│ d) -(-a) e) -│-a│
I am totally confused about absolute values and do not understand this question.
Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
If  is a negative real number, then  must be a positive real number.
Let's look at the definition of absolute value:
When you read this definition, read  as "the opposite" of  rather than "negative" or "minus" . I find it much less confusing to think of it in this way.
Part b is  . In part a of the problem we established that must be a positive real number. Looking at the definition of absolute value -- if the thing inside of the absolute value bars is positive, then the value of the absolute value function is identical to the value of the thing inside. Since is positive, the absolute value of must be which is positive.
Part c. First determine  . We know  to be negative, therefore, using the definition, the absolute value of must be the opposite of or  . From part a of the problem we know that is a positive number. Hence is positive. But part c asks for  . This is the opposite of a positive number, i.e. a negative number.
Part d. We know from part a that is a positive number. Part d asks for the opposite of a positive number, to wit, a negative number.
Part e. We know from part b that is a positive number. Just like in part d, the opposite of a positive number is a negative number.
John
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website! Hint: The absolute value of any number is ALWAYS positive. So |a| is ALWAYS positive and |-a| is ALWAYS positive. Let me know if this clears things up a bit.
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