Question

Absolute Value (Question on comment)

Answer 1

Hello.

Recently I “discovered” that I don’t know very well problems with absolute value!
Example:
Why
\[\LARGE |x-1|=2x+1 \]
Is equal to 0 and not -2 too...

And I’m having really trouble by defining X element of what..

Example:
\[\LARGE |3x+5|<8 \]
\[\LARGE -13<3x<3 \]
\[\LARGE -\frac{13}{3}<x<1 \]
Now X element of what?
\[\LARGE x\in (-\infty ,1)\cup \left(-\frac{13}{3},+\infty\right) \] ?? :(
Another one...
\[\LARGE |5x+4|\geq 3\]
\[\LARGE -3\geq5x+4\geq 3\]
\[\LARGE -7\geq5x\geq -1\]
\[\LARGE -\frac75\geq x\geq-\frac15\]
Now I gues that:
\[\LARGE x\in \left(-\infty,-\frac75\right]\cup \left[-\frac15,+\infty\right) \]
but multiple choices on book are..

\[\LARGE A) \quad (-\infty ,3) \cup \left( \frac{15}{2},+\infty \right)\]
\[\LARGE B)\quad \left(\frac15,+\infty\right)\]
\[\LARGE C) \quad \left(-\infty ,-\frac75\right)\]
\[\LARGE D) \quad \left(-\infty ,-\frac75\right)\cup \left(\frac15 ,+\infty\right)\]
I'm super confused ! :(

This is causing me problems \[\LARGE x\in (??)\]

Answer 2

for your last example, i would agree with your answer
so does wolfram
http://www.wolframalpha.com/input/?i=abs%285x%2B4%29+%3E%3D+3

Answer 3

actually, I checked wolframa only about the first one... but I don't know...
shouldn't it be like example:
|x+2|=3
x+2=3 x+2=-3
x=1 x=-5
? :(

Answer 4

for the problem
\[-\frac{13}{3} <x <1\]
x is in (-13/3 , 1)

Answer 5

ahh... so it stops , and doesn't go till to infinity... so it's not \[\LARGE \cup \quad \quad \quad it's \quad \quad \quad \cap\] isn't it ? :(