Question

Hello.

Trying to exercise "simple" absolute value problems..
Here I got stuck again!

Answer 1

\[\LARGE \begin{array}{l}6.\,\,\,\,\, - 3\left| { - 2x + 4} \right| \le 4\\\\\frac{{ - 3\left| { - 2x + 4} \right|}}{{ - 3}} \ge \frac{4}{{ - 3}}\\\left| { - 2x + 4} \right| \ge - \frac{4}{3}\\ - \left( { - \frac{4}{3}} \right) \ge - 2x + 4 \ge - \frac{4}{3}\\\frac{4}{3} - 4 \ge - 2x \ge - \frac{4}{3} - 4\\ - \frac{8}{3} \ge - 2x \ge - \frac{{16}}{3}\\\frac{8}{3} \le 2x \le \frac{{16}}{3}\\\frac{8}{{3 \cdot 2}} \le x \le \frac{{16}}{{3 \cdot 2}}\\\frac{8}{6} \le x \le \frac{{16}}{6}\\\frac{4}{3} \le x \le \frac{8}{3}\\x \in \left[ {\frac{4}{3},\frac{8}{3}} \right]\end{array}\]

is this wrong or not...
is it is, where...
In the web it says that answer is
(- infinity , +infinity)
but I get a different answer :(

Answer 2

I forgot to mentioned that this is not solved in web.. (steps) I did them :( ... Thanks

Answer 3

yes... although I don't have |A| > |B|
I have |A|>B
but that it doesn't matter...

from
|A|>B

-B>A>B
is the same as
A>B or A<-B

and I think that's what I did. :(

Answer 4

http://www.analyzemath.com/AbsEqIneq/answers_AbsEqIneq.html
problem nr. 7

Answer 5

Your inequality is true for every x.

−3∣−2x+4∣<= 0 for all x so it is less than 4.

Answer 6

Here's the intuitive explanation.
−3*∣−2x+4∣ ≤4
That absolute value portion of the equation is always non-negative. Multiplying by a negative number will yield a negative, therefore the result will be less than 4.

However, I'm not sure which part of your workout is wrong yet.

Answer 7

but how.. why?

...
Honestly I'm confused now :(
−3∣−2x+4∣<= 0 ??
it's −3∣−2x+4∣<= 4
:)
what's wrong with my answer.. :( I need some help here.

Answer 8

The solution is I said before is
\[
-\infty < x <\infty
\]

Answer 9

according to your solution, x=0 is not in there but it does work...

Answer 10

@eliassaab is correct.

Answer 11

Nevermind. I found the mistake you made. It was at this step.
|-2x+4| >= -4/3
When it's a greater than sign, I can rewrite it as
-2x+4 >= -4/3 OR -2x+4 <= -4/3

You used the rule for when it is a less than sign.

Answer 12

@dpaInc I have no doubts that eliassaab might be wrong... but I want to know how this should be solved thenn... only by observation? :(

Answer 13

\[-\frac{-4}{3} \ge -2x+4 \ge -\frac{4}{3}\]
This step of your work was incorrect.

Answer 14

Instead you should have
\[-2x+4 \ge \frac{-4}{3} or -2x+4 \le \frac{-4}{3}\]

Answer 15

@SmoothMath what you're saying it doesn't make sense now !! ...
\[\LARGE -2x+4\geq -\frac43\] or \[\LARGE -2x+4\leq -\frac43\]
is the same as:
\[\LARGE -\frac43\geq -2x+4\geq -\frac43 \]
which is exactly what I did...