Solve |x + 6| = 12.
A. 6
B. -18
C. {6, -18}
D. No Solution

Question

Solve |x + 6| = 12.
	A.	6
	B.	-18
	C.	{6, -18}
	D.	No Solution

turingtest · Answer

we get two equations when we have an absolute value, because there are two possibilites

turingtest · Answer

$$|x+6|=12$$implies that either$$x+6=12$$or$$x+6=-12$$

anonymous · Answer

-12=x+6           x+6=12

-12-6=x            x=12-6

-18=x                x=8

turingtest · Answer

solve each equation separately and you will have your answer

anonymous · Answer

@TuringTest  I'm having a doubt ... example:

if I have this equation:

$$\Large |x-2|>7$$

when I start solving, after taking off the absolute value should I change - into +

like:

-7>x+2>7

?? :(:(

or do I have to leave it minus like it is ?

turingtest · Answer

@Kreshnik 
1)please don't cut me off in the future, I had this under control and wanted to $not$ provide the answer

-in answer to your question
$$|x-2|>7$$implies that either $$x-2>7$$or$$x-2<-7$$

turingtest · Answer

only if the sign is$$x<y$$can you write$$-y<x<y$$(provided that y>0}

turingtest · Answer

sorry, typo* should have been$$|x|\le y\implies -y\le x\le y$$

anonymous · Answer

... and if  $$\Large x\neq y$$
 x=1  y=2 

1<2
-2<1<2
I think yes :(


@TuringTest  I do really apologize for interrupting , It won't happen again !

turingtest · Answer

but$$|x|\ge y\implies x\ge y\text{ or } x\le-y$$

turingtest · Answer

it's fine, no worries ;D
I'm just trying to prevent those who would keep trying to avoid explanation, and I think this particular asker is a culprit ;)

anonymous · Answer

ahh... obviously, he doesn't even try to solve those, and I think that will revenge him in the future! ... he won't get nowhere without trying ! ...  @TuringTest Thanks for explaining it.  I apologize again ;)

anonymous · Answer

Yup, I think so @TuringTest and @kreshnik - I'll take care of that. Btw, great work from both of you here.