Question 273676: Suppose that a is a negative real number, determine whether which of the following is positive or negative.
a) -a
b) |-a|
c)-|a|
d)-(-a)
e)-|-a|
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! If 'a' is negative, then -a is the opposite of a negative number which means that -a is positive. Eg: if a=-2, then -a=-(-2)=2
Remember that the absolute value of ANY number is ALWAYS positive. So |-a| is positive regardless if 'a' is positive or negative.
On the flip side, since absolute values are always positive, the opposite of an absolute value is negative. So -|a| is negative since |a| is positive.
Likewise, since |-a| is also positive (see above), -|-a| is negative since -|-a| is the opposite of |-a|.
|
|
|
