Regarding a practice question in Prepswift

[user3399]

I have been working with the PrepSwift material and am confused with the solution for this question:

Quantity A Quantity B
∣x∣ ∣(∣x∣)∣

My line of reasoning:

when x=0, both sides 0

when x> 0
A: +x
B: +x , |x| agin +x

when x<0
A: - x
B: | - x | = x

So, the answer should be D.

for absolute values should we just take numbers on the number line and compare or use this?

because for example | x | / x has two solutions 1 or -1

[cylverixxx]

It’s hard to decipher what you have written. Can you post a picture of the actual question?

[user3399]

sure, this one!

[cylverixxx]

Okay i see

@user3399

when x<0
A: - x
B: | - x | = x

Why do you say this? We know that the output of |x| is always positive and repeatedly applying the absolute value shouldn’t change its sign right?

[user3399]

I think | x | is +x when x > 0 and -x when x < 0

[cylverixxx]

The graph of -x when x < 0 is above the y axis. Similarly, the graph of x when x > 0 is also above the y axis. |x| is always non-negative for all real values of x .

[user3399]

thank you!