Thursday, June 9, 2016

High School Math Solutions – Inequalities Calculator, Absolute Value Inequalities Part I

Last post, we learned how to solve rational inequalities. In this post, we will learn how to solve absolute value inequalities. There are two ways to solve these types of inequalities depending on what the inequality sign is. Let’s see how to solve them . . .

Case I (< or ≤):
Given |x|<a, 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: -a<x<a.
The same goes for ≤. Just substitute ≤ for < and fill in the circles in the number line.

Case II(> or ≥):
Given |x|>a, 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.


NOTE: Remember to carry out any algebraic manipulations outside of the absolute value before continuing, for example:
2|x|-2>4
|x|>3
ANOTHER NOTE: Make sure a is positive or else there is no solution.


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

21 comments:

  1. 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.
    [email protected] User Accuess

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

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

    ReplyDelete
  4. I 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

    ReplyDelete
  5. Completely. 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
  6. Uncommon Discussion and I concur with this post since I've been an understudy in an MBA last semester, you share this data really established a debt of gratitude is in order for refreshing news about understudies I bookmarked your blog for the most recent updates. Wesley Snipes Distressed Jacket

    ReplyDelete
  7. All of our custom term paper writing service will always be 100% unique and authentic work composed by an essayist on our writing team as plagiarism is a crucial area when it comes to seeking custom dissertation writing services in our firm.

    ReplyDelete
  8. One should know which company has the best writers whose essay is free from grammatical errors. Grammatical errors reduce the quality of a custom paper especially those who want to pre written research paper and those seeking for custom assignment services.

    ReplyDelete
  9. This content is very good. Thank you for this great website.

    คาสิโนออนไลน์ที่น่าเชื่อถือและมีความเป็นมืออาชีพที่สุดในตอนนี้
    โปรโมชั่นGclub ของทางทีมงานตอนนี้แจกฟรีโบนัส 50%
    เพียงแค่คุณสมัคร สล็อตออนไลน์ กับทางทีมงานของเราเพียงเท่านั้น
    ร่วมมาเป็นส่วนหนึ่งกับเว็บไซต์คาสิโนออนไลน์ของเราได้เลยค่ะ
    สมัครสล็อตออนไลน์ >>> Goldenslot
    สนใจร่วมสนุกกับ คาสิโนออนไลน์ คลิ๊กได้เลย
    มีทั้งคาสิโนออนไลน์ หวยออนไลน์ ฟุตบอลออนไลน์ สล็อตออนไลน์ และอื่นๆอีกมากมาย

    ReplyDelete
  10. Thanks for your submission. I also think that laptop computers are getting to be more and more popular right now, and now are

    sometimes the only sort of computer found in a household. This is due to the fact that at the same time potentially they are becoming

    more and more economical, their processing power is growing to the point where they’re as strong as desktop computers from just a few

    years ago.
    quickbooks suppport
    install apps quickly

    ReplyDelete
  11. One of the most noticeable things a visitor sees on your website is your logo. Your logo will be in most cases the influencing factor regarding whether your website is worth the visit or not. So, you need to have a great logo design which makes the visitor stop for a moment.

    ReplyDelete
  12. Students seek professional Custom Papers Writing assistance from Top Rated Term Papers Writingcompany to accomplish any type of essay assigned to them. When you request for urgent Professional Custom Research Paper, they strive to meet your professors’ requirements.

    ReplyDelete
  13. This is my first time I visit here. I found such a significant number of engaging stuff in your blog, particularly its exchange. From the huge amounts of remarks on your articles, I surmise I am not by any means the only one having all the relaxation here! Keep doing awesome. Organic Moisturizing Cream Xord Cosmetics

    ReplyDelete
  14. Bu benim ilk ziyaretim. Blogunuzda bu kadar önemli ilgi çekici şeyler buldum, özellikle takası.
    Betvole
    Betvole
    Elexbet
    Betebet
    Betebet
    Betpas
    Betpas
    Betpas

    ReplyDelete