If x=|x| then don't we already know that x is positive? If that's the case then isn't #1) x=even irrelevant? Doesn't x HAVE to be positive?
I think you tripped up on what is given and what is to be found.
You are asked: Is x = \sqrt{x^2}?
You are asked: Is x equal to |x|?
The question doesn't tell us this. It wants us to answer whether it is true.
When is x=|x|? When x is non negative. If the statement tells us that x is non negative, we can say that yes, x is equal to |x|. Statement 2 tells us that x is positive. So it is sufficient alone.
VeritasPrepKarishma wrote:
WholeLottaLove wrote:
x = \sqrt{x^2}
So basically, what this says is the following:
x = |x|
So, x = x or x = -x
Firstly, this means that, for example:
x=5 or x=-5
Correct?
I guess where I get tripped up is here:
Let's say x=14 and x=|x| so x=x or x=-x
so
x=14
OR
x=-14
With #2 we are told that x is positive and the stem tells us that x=|x|. But isn't that unnecessary? doesn't x=|x| imply that x is positive anyways? Or, if this makes any sense, if x=x or x=-x then couldn't 14=-x?
So basically, what this says is the following:
x = |x|
So, x = x or x = -x
Firstly, this means that, for example:
x=5 or x=-5
Correct?
I guess where I get tripped up is here:
Let's say x=14 and x=|x| so x=x or x=-x
so
x=14
OR
x=-14
With #2 we are told that x is positive and the stem tells us that x=|x|. But isn't that unnecessary? doesn't x=|x| imply that x is positive anyways? Or, if this makes any sense, if x=x or x=-x then couldn't 14=-x?
I think you tripped up on what is given and what is to be found.
You are asked: Is x = \sqrt{x^2}?
You are asked: Is x equal to |x|?
The question doesn't tell us this. It wants us to answer whether it is true.
When is x=|x|? When x is non negative. If the statement tells us that x is non negative, we can say that yes, x is equal to |x|. Statement 2 tells us that x is positive. So it is sufficient alone.