# Writing inequality in interval notation

• Aug 24th 2011, 04:58 PM
Kenny95
Writing inequality in interval notation
I'm having issues remembering how to do this.

Ok first of all, I'm not sure how to write absolute value signs on here. And Im also not sure how to write greater/less or equal to inequality signs.

But what I'm trying to figure out is (abs) x + 2 (abs) is greater than or equal to 6.
(and im using the (abs) as the absolute value bars sense i dont know how else to write them)

I know you solve it like this: x+2 greater than or equal to -6, or, x+2 greater than or equal to 6. And you get x is greater than or equal to -8 and x is greater than or equal to 4. So how do i write this in interval notation?

Sorry If ive made it confusing by not being able to properly write this on here.
• Aug 24th 2011, 05:06 PM
Plato
Re: Writing inequality in interval notation
Quote:

Originally Posted by Kenny95
I'm not sure how to write absolute value signs on here. And Im also not sure how to write greater/less or equal to inequality signs.

But what I'm trying to figure out is (abs) x + 2 (abs) is greater than or equal to 6.
(and im using the (abs) as the absolute value bars sense i dont know how else to write them)

PLEASE learn to use even the most basic LaTeX on this site.
[tex]|x+2|\le 6 [/tex] gives \$\displaystyle |x+2|\le 6 \$
Is that so hard to learn?
• Aug 24th 2011, 05:08 PM
Kenny95
Re: Writing inequality in interval notation
Ok, bro. Sorry man. I didnt even know that existed. I didnt mean to anger anyone
• Aug 24th 2011, 05:13 PM
Kenny95
Re: Writing inequality in interval notation
Look, sorry I wasn't familiar with this Latex stuff. I'm new to all of this. I'll definitely go over everything in that link you posted so this will not happen again.
• Aug 24th 2011, 05:13 PM
Plato
Re: Writing inequality in interval notation
Quote:

Originally Posted by Kenny95
Ok, bro. Sorry man. I didnt even know you had anything like that. I didnt mean to anger anyone

You angered no one. Least of all me.
The point being if we cannot be sure of the reading of the question then it waste time composing an answer which has nothing to with the OP.
• Aug 24th 2011, 05:16 PM
Kenny95
Re: Writing inequality in interval notation
Yes, I understand, Plato. I was honestly clueless about this Latex stuff. I thought there had to be something you guys had to write equations etc but i wasnt sure
• Aug 24th 2011, 05:22 PM
Kenny95
Re: Writing inequality in interval notation
\$\displaystyle |x+2|\geq \$ 6

Ok, I got it now. Sorry about all of this. How do you write this in interval notation form after solving it?

thanks
• Aug 24th 2011, 08:05 PM
SammyS
Re: Writing inequality in interval notation
Well, first you solve it.
• Aug 25th 2011, 02:28 AM
HallsofIvy
Re: Writing inequality in interval notation
Good advice! And to start solving it, remember that, without knowing x, we cannot know if |x|= x or |x|= -x. So try both.

Can you solve \$\displaystyle x+ 2\ge 6\$? What about \$\displaystyle -(x+2)\ge 6\$? And for what values of x do those apply?

You could also do a "geometric" solution. Geometrically, we can interpret "|x- y|" as "distance between points x and y". So we can interpret \$\displaystyle |x+ 2|= |x- (2)|\ge 6\$ as saying that the points, x, satisfying this are points on the number line whose distance from -2 is greater than or equal to 6. Where are those?