**Case I (< or ≤):**Given , we read this as “x is less than a units for 0.” On a number that looks like:

The red line is the solution for x. Remember because it is “less than,” a is not included in the points (this is why the circle is not filled in).

So we rewrite

The solution is in this form: .

The same goes for ≤. Just substitute ≤ for < and fill in the circles in the number line.

__Case II(> or ≥):__Given , we read this as “ x is more than a units from 0.” On a number line, that looks like:

The red line is the solution for x. Remember because it is “greater than.” A is not included in the points.

So we rewrite

The solution is 2 inequalities, NOT one. It is in the form: x<-a or x>a.

The same goes for ≥. Just substitute ≥ for > and fill in the circles in the number line.

**Remember to carry out any algebraic manipulations outside of the absolute value before continuing, for example:**

__NOTE:__**Make sure a is positive or else there is no solution.**

__ANOTHER NOTE:__Let’s see some examples . . .

First example (click here):

Notice that the algebraic manipulations to be done are inside the absolute value, so that is done last.

Last example (click here):

That wasn’t too complicated. Next post, we will learn how to solve absolute value inequalities with two absolute value expressions in it. Make sure you practice because next post the problems will become trickier.

Until next time,

Leah

JioTV

ReplyDeleteMyJio

Vidmate

Very well written article. It will be helpful to everyone who employee it, including me. Keep up the good work - can't wait to read more posts.

ReplyDelete[email protected] User Accuess

Thank you for taking the time to publish this information very useful! ingilizce kursu

ReplyDeleteI recommend you to check this blog article for some tips on how to write dissertation. It could be interesting

ReplyDeleteI think this is an informative post and it is very useful and knowledgeable. therefore, I would like to thank you for the efforts you have made in writing this article. beşiktaş ingilizce kursu

ReplyDeleteCompletely. I truly miss it and I realize I've lost alot of solidarity due to being sick for a long time and not having the capacity to lift. I feel feeble as poop now. Certainly, muscle memory is a thing however it's the mental part of returning down to bring down numbers and battling even with that which is getting to me. In any case, I plan on beginning once more Cheap Dissertation Help Services, gradually yet most likely, in 8 days. Wish me karma. I simply continue pondering the incredible inclination, the extraordinary rest, certainty, everything...

ReplyDelete