Tricky DS Please help

[NL]

Sorry, I still failed to take a shovel and dig. Will do.

[jnelson0612]

Sorry, I still failed to take a shovel and dig. Will do.

:-)

[NL]

* If you just shuttle the absolute-value bars to the other side of each of these equations, the resulting equations, x + 3 = |4x - 3| and x + 1 = |2x - 1|, have two solutions each.

That’s because only negative numbers need to get into | | to be equal with the other side, (of course I didn’t know it until you pointed out.)

Yeah, sometimes I jumped to conclusions without considering a lot of other cases. But I see your point here. Nice!

[RonPurewal]

Yeah, sometimes I jumped to conclusions without considering a lot of other cases. But I see your point here. Nice!

In general, you can avert a lot of mental acrobatics by just working out the problem.
Unless something is genuinely going to take 5+ minutes to do (an extreme rarity on this test), it's best just to do the work, unless you know exactly how everything is going to turn out.

[NL]

Re-written questions:

E.g. 1: Bad a-Good a
(Changing statement 1)
Is a >0?
(1) |3a| = a-8
(2) (a-1)^9 > -1

Hehe, the re-written statement (1) is still...bad. Sorry Ron. But why didn't you tell me? I didn’t test the numbers carefully. It should be written like this:

(1)|a| = 3a-8
or something like these also work:
|1/3a| = 1/2a -1
|2a| = 3a-8
|10a| = 100a-1/100
etc.

Something looking like these don’t work:
|1/2a| = 1/3a-1
|1/2a|= -1/3a-1
|3a| =2a-8
|100a|= 10a- 1/100
etc.

Do you know why?

P/s: I edited the question 1 again in the previous post and provided answers. Please let me know any other problems in them. Thanks.

[RonPurewal]

Since this discussion has evolved into something completely unrelated to the problem in the thread, I'd suggest that you move it to the general math folder if you want to continue having it.

Thanks.

[NL]

This is called "brute force", but I have no choice. So "just do the work"!

[RonPurewal]

Something like that.