Question regarding absolute value

[ErikM411]

In a study-hall from Feb 18-2010. There is a question about absolute values (for question, see image attached)

What I don't understand is why "-3/7" yields a "fake solution". The absolute value of -3/7 is 3/7. So why is this invalid?
-3 = |3|. Why isn't it the same here with -3/7 = |3/7|?

[RonPurewal]

The absolute value of -3/7 is 3/7.

that ^^ is true, but it's irrelevant here: we don't have an equation that says |-3/7| = 3/7. if that were what we actually got, then the corresponding solution would be perfectly valid.

here, we have an equation that says |3/7| = -3/7. that clearly doesn't work, as "|thing| = negative" is impossible regardless of what the thing is.

[ErikM442]

The absolute value of -3/7 is 3/7.

that ^^ is true, but it's irrelevant here: we don't have an equation that says |-3/7| = 3/7. if that were what we actually got, then the corresponding solution would be perfectly valid.

here, we have an equation that says |3/7| = -3/7. that clearly doesn't work, as "|thing| = negative" is impossible regardless of what the thing is.

cool, thanks, that makes sense. is it weird for you responding to a question you covered 5 years ago. do you ever go "i remember drawing that green arrow back in 2010"

[tim]

[RonPurewal]

do you ever go "i remember drawing that green arrow back in 2010"

i'm lucky if i remember something i wrote last month.