solve for \(x\).

- mathmath333

solve for \(x\).

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- jamiebookeater

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- mathmath333

\(\large \color{black}{\begin{align} \sqrt{x^2}

- anonymous

Need help @mathmath333 ^.^

- anonymous

If you think im new and dont know much about OS this is my alt account .-. my original is @just_one_last_goodbye

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## More answers

- anonymous

Let's take a look... ^_^

- anonymous

but @mathmath333 I'm being monitored by mods and cant give a direct answer so please stay I need your participation

- anonymous

First we need to find the "real region" of the problem

- anonymous

\[\sqrt{x ^{2}}\] is real to what?

- anonymous

@mathmath333 u there?

- anonymous

what have you got math?

- mathmath333

i have got \(x>-1/2\) and \(x>0\)

- anonymous

It is real to \[(x ^{2}) \ge 0\]

- anonymous

@mathmath333 thats the answer x > -1/2 is the solution

- anonymous

x>-1/2 covers x>0 also, so answer is x>-1/2

- anonymous

\[[Solution: x > -\frac{ 1 }{ 2 }\]
\[[Decimal: x > -0.5]\]
\[[Interval Notation: (-\frac{ 1 }{ 2 }, \infty) ]\]

- anonymous

Oh hey @wio huge fan of your extension that you made for OS ^.^ im currently using all of them

- mathmath333

but the common region between \(x>0.5\) and \(x>0\) so why not \(x>0\)

- anonymous

x>-0.5 not x>0.5

- mathmath333

yea i mean \(x>-0.5\)

- anonymous

You can split it up: \[
x\lt x+1 \\
-x\lt x+1
\]The first equation will be true for all real \(x\), and so only the second equation matters.
That equation leads to: \[
0\lt 2x+1 \implies -\frac 12 \lt x
\]

- dan815

|dw:1435865650234:dw|

- anonymous

@Captain_America_Army Glad you like it.

- dan815

sqrt(x^2) is another way to write the abs value of x

- dan815

|dw:1435865730882:dw|

- mathmath333

how do u draw that

- dan815

draw the y=ABS(x) and the line y=x+1

- dan815

like wio mentioned abs(x) can be split into 2 lines -x and x

- mathmath333

ok thnx every one

- anonymous

Where did the \(0\lt x\) come from?

- anonymous

That was a good question math, why x>-0.5 and not x>0

- mathmath333

but desmos did this https://www.desmos.com/calculator/lnftaoee2g

- dan815

my drawing is so bad actually lol

- dan815

they are parallel lines they wont intersect

- dan815

but u get the point

- mathmath333

\(\sqrt{x^2}\implies x>0 ,\ \ and \ \ x<0\)

- anonymous

In my equations, the first one assumes \(0\lt x\) and finds out \(x\in (0, \infty)\).
The second one assumes \(x\lt 0\) and finds out \(x\in (-0.5, 0)\).

- dan815

|dw:1435866160067:dw|

- anonymous

We union these intervals (because absolute value splitting up of problems is a union). We also check that \(x=0\) works. So our result is \(x\in (-0.5, \infty)\).

- anonymous

thanks wio

- anonymous

o.o working in the middle of OS math legends.... ~honored~

- dan815

|dw:1435866195634:dw|

- mathmath333

i get confused where to choose common region \(\cap\) and where to choose union region \(\cup\)

- mathmath333

in math questions haha

- anonymous

^ agreed

- dan815

i remember when you see a U its union

- dan815

and upsinde down U looks kind of like n for n-tersect

- dan815

u n

- anonymous

looks like a man with no hair to me .-.

- dan815

it actually is n flipped in this font

- dan815

180 deg rotation

- mathmath333

dan i got this https://www.desmos.com/calculator/vlaerg67rk

- dan815

yep

- anonymous

Dear math, please stop asking us to find your \(x\), he is gone and he's never coming back. just accept it. xD

- anonymous

~face palm~ smh >.< "math jokes"

- mathmath333

no he is back

- dan815

shes gonna eat \[\pi \] and get fat now

- anonymous

what u gotta say to that Muk xD

- anonymous

##### 1 Attachment

- anonymous

I am also going to eat a\[\pi z^2 a\]

##### 1 Attachment

- anonymous

~yawn~ so instead of helping people... we are here making math jokes... that are more dry than the desert? nice ladies just nice.... http://www.joesdaily.com/wp-content/uploads/2014/11/joker-clapping.gif

- anonymous

:)) xD

- anonymous

.-. Hey Sexy Lady ~points @mukushla ~ Opa Opa Opa Gangnam style

- mathmath333

|dw:1435867862718:dw|

- anonymous

.o. @mathmath333 show me how to do that ;-; I've asked everyone and they dont want to show me

- anonymous

That mod "TkHunny" =.= banned me for a week for posting external links

- anonymous

will 10 owl bucks do the job?

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