Multiple-choice problem why is this the answer?

[IntegrateMe]

For any real numbers x, y, and z, if the equation:

|z| + y = x

is to be satisfied, which of the following must be true?

(A) x is greater than or equal to y
(B) x is greater than or equal to z
(C) x is less than or equal to y
(D) x is less than or equal to z
(E) y is greater than or equal to z

The answer is (A), i just don't know how to arrive there.

Thanks.

 

[iratern]

Well fist of all what are your thoughts on the answer? What is your reasoning? You should show us your attempts at solving the question.

 

[matt_crouch]

try rearranging the equation to make |z| the subject

 

[IntegrateMe]

|z| = x - y

Is there any way to get rid of the absolute value symbol around the z?

 

[iratern]

absolute value is defined as

if x>=0 then |x|= x,

if x<0 then |x|= (-x)

which basically means that absolute value is the numbers distance from the origin of the number line a.k.a any number within the absolute value comes out as a positive number (except 0 which, obviously, is still 0)

 

[IntegrateMe]

Can you just tell me how to do the question?

 

[cesiumfrog]

Is |x| positive, or negative?
Is something equal to |y| potentially greater than or less than zero or both?

 

[IntegrateMe]

|#| is going to be greater than or equal to 0, i suppose.

 

[Mark44]

|#| is going to be greater than or equal to 0, i suppose.

Yes.
Now, since |z| = x - y, what does that tell you about the expression x - y?

Can you just tell me how to do the question?

Per the rules of this forum, we don't do that. We'll help you with it, but you have to do the work.

 

[IntegrateMe]

I'm trying to understand what you guys are saying but i usually comprehend things if i just see the answer and work backwards.

|z| = x - y tells me that |z| is going to be equal to x - y

 

[IntegrateMe]

Oh, wait. I think i catch it:

If the |z| is always going to be greater than or equal to 0, that means x must be greater than or equal to y or else we will form a negative number on the right side of the expression?

I feel stupid now. Thanks for the help guys.

 

[novop]

I think you understand, but just to make sure, it doesn't matter if the right side is negative or positive. If y is negative, and you add the absolute value of z (which is always positive), then x is still greater than y, even if both x and y are negative values.

 

[IntegrateMe]

Oh, i see what you're saying novop. That makes sense. I guess this question is more conception more than anything.

Thanks a lot!

 

[Mark44]

I'm trying to understand what you guys are saying but i usually comprehend things if i just see the answer and work backwards.

Well, of course, but as I already mentioned, that's not the way we do things here. Maybe it's easier to comprehend if you see the answer and can work backwards, but you learn better by doing the work yourself, rather than seeing someone else's final result.