ShmoopTube

00:02

Put this in your calculator and shmoop it.

00:06

If the absolute of x plus y equals the absolute

00:08

value of x plus the absolute value of y, then x and y must be which of the following?

00:14

I. Positive II. Negative

00:15

III. One positive and one negative Here are the potential answers...

00:23

Alright, we have one of those multiple part questions where we have to test choices I, II, and III.

00:27

Whenever we see those straight vertical lines,

00:30

also known as the absolute value sign. We know the answer that comes out of those

00:33

lines will always, always be positive. So, let's test each case by plugging in numbers for x and y.

00:40

Case I: Both x and y are positive.

00:44

If x = 5 and y = 5, the absolute value of 5 + 5 = 10, and the absolute value of 5 plus

00:51

the absolute value of 5 is also 10. Check, this one works.

00:55

Case II: Both x and y are negative.

00:58

If x = -5 and y = -5, then the absolute value of negative 5 plus negative 5 = 10, and the

01:05

absolute value of negative 5 plus the absolute value of negative 5 equals 10. Check.

01:10

Case III: x and y are opposite signs.

01:14

If x = 5 and y = -5. The absolute value of 5 plus negative 5 equals zero.

01:22

and the absolute value of 5 plus the absolute value of negative 5 equals 10.

01:27

Ehh, this one's a no-go.

01:30

Only cases I and II make the original premise true, so (D) is the correct answer.

Full Transcript