Thursday, June 9, 2016

High School Math Solutions – Inequalities Calculator, Rational Inequalities

Last post, we talked about solving quadratic inequalities. In this post, we will talk about rational inequalities. Let’s recall rational functions are an algebraic fraction that contain polynomials in the numerator and denominator. Solving rational inequalities is a little different than solving quadratic inequalities. Both share the concept of a table and testing values.

Let’s see how to solve rational inequalities.

Here the steps:
  1. Move everything to one side of the inequality sign
  2. Simplify the rational function 
  3. Find the zeros from the numerator and undefined points in the denominator
  4. Derive intervals
  5. Find the sign of the rational function on each interval
  6. Select the proper inequality

Let’s go through our first example step by step to understand the concept better.

Here’s our first example (click here):
Step 1: Move everything to one side of the inequality sign
Make sure you combine everything into one rational function.

Step 2: Simplify the rational function
It’s already simplified. Nothing to cancel out.

Step 3: Find the zeros from the numerator and undefined points in the denominator
-3x+12=0                                                        x-3=0
x=4                                                                     x=3
          Zero                                                                     Undefined point

Step 4: Derive intervals

Step 5: Find the sign of the rational function on each interval

Table Header x\lt3 3\ltx\lt4 x\gt4
\frac{-3x+12}{x-3} \frac{-3(0)+12}{(0)-3}=-4 \frac{-3(3.5)+12}{(3.5)-3}=3 \frac{-3(5)+12}{(5)-3}=-\frac{3}{2}
Sign \quad\quad\quad\quad- \quad\quad\quad\quad+ \quad\quad\quad\quad-

We changed the format of the intervals to inequalities. We pick a number in the interval, plug the number in the rational function and see what sign the answer is (negative or positive).

Step 6: Select the proper inequality
We refer back to the original inequality and see which inequality satisfies the original inequality. We are looking for a number that produces a negative number. We refer back to the table and see that x<3 and x>4 satisfy this.

Alright, that was a mouthful. Let’s see some more examples now…

Second example (click here):

Last example (click here):

Make sure you double check your work for calculation errors because that is where it’s very easy to make a mistake. For more practice, check out Symbolab’s practice.

Until next time,



  1. Solving rational inequalities is a little different than solving quadratic inequalities. writing fellowship personal statement is the best option.

  2. There are many accredited nursing schools in California. If you live in the southern California area here are a few nursing schools you might want to consider. visit the site

  3. A personal declaration is a purposefully crafted essay that offers you the opportunity to "sell" yourself by describing your best characteristics and strengths.mph statement of purpose read here

  4. To know importance of education, everybody ought to scan your post. Now days, one and all remains busy in his job or work and it's terribly troublesome to continue their academic carrier except through on-line channel. explore more

  5. Editing your personal statement for university submission is often difficult. This article is a practical guide packed with inspirational and easy to follow advice on how to edit a personal statement - this article will tell you everything you need to know, regarding editing and building tension in your writing. site.

  6. Thank you so much for sharing such useful and interesting information. Your website is highly effective and contains worthy content. I find it more enjoyable than any other show.
    bloons tower defense 5

  7. ADM-201 exam question Awesome blog. I would love to see true life prepared to walk, so please share more informative updates. Great work keeps it up.

  8. I see different contrasts on here, for example, the accentuation on naming laws, for example, distributive, commutative and affiliated utilized in ordinary counts, essay service -, and a practically absolute nonattendance of any inquiries in the field of what used to be called connected science and hypothetical mechanics, which was separated into statics and elements.

  9. You have used the commends to hack this program and it is the same from which I have also done out class jackets before. It is the only idea to get access through the data that most of the users are looking for.

  10. Inequalities can mostly be treated as an equals sign. Instead of giving a exact value for a variable, they give a range of possible values. Are you facing Alliant Capital Management Debt Collection Harassment? Give us a shout today & get rid of phone harassment from this agency etc.

  11. I like this website pretty much. Great info. Hi and thanks for the web blogs. Consumer attorney

  12. I just want to thank you to share your information on your blog; this is a simple and useful. relocating to Mesa Arizona

  13. This calculator can graph an inequality in two variables by shading the screen above or below the graph of an equation. Where Can I Pay Someone to Do My Assignment

  14. Pretty sure you can as well. You can try and refer to your manual, or if you don't have it, try and check the internet for some answers on how it's done. Assignment Service Online

  15. inequalities in equations, just treat them as equals signs. The only exception is when you multiply both sides of the equation by a negative number. UK dissertation help service

  16. Our declaration to providing the best customer experience when it comes to the best custom essay writing service are guided by these principles we entrench daily in our delivery for the best online essay writing service firm.

  17. thank you.
    โปรโมชั่นGclub ของทางทีมงานตอนนี้แจกฟรีโบนัส 50%
    เพียงแค่คุณสมัคร สล็อตออนไลน์ กับทางทีมงานของเราเพียงเท่านั้น
    สมัครสล็อตออนไลน์ >>> Goldenslot
    สนใจร่วมสนุกกับ คาสิโนออนไลน์ คลิ๊กได้เลย
    มีทั้งคาสิโนออนไลน์ หวยออนไลน์ ฟุตบอลออนไลน์ สล็อตออนไลน์ และอื่นๆอีกมากมาย

  18. Our writing company is the most college research papers company and we are always ready to answer any form of questions which may come up especially those seeking for best writing services online.

  19. ​The team consists of PhD experts of Assignment help provide the best quality services. Thanks for providing me such as professional knowledge. For any concern directly get into touch with our expert 24*7 with cheap prices, Assignment Help.

  20. Extraordinary stuff and I guess that this sort of post is stunning completely from us. It's my happiness to peruse your post. It is an edifying and blending and most elite pursuit of my life. Custom Logo Design In California

  21. Excellent post and wonderful blog, Very good writing a university college and collecting information on this topic .I really like this type of interesting articles keep it up.
    Assignment Help Australia

  22. You may need to check out this little blog article on how to write a qualitative research and how to do it right. This could be helpful

  23. Your blog content is perfect. Thank you so much for sharing us such a nice kind of info.
    Assignment Help US
    Java assignment help

  24. Allassignmenthelp is your academic caretaker. Our online assignment assistance is one of the most sought after in the US and other countries and you should give us a chance to assist you. SWOT Analysis of Apple

  25. Do you have a problem in writing your maths homework? Need math homework help USA? Then take help from, it provides math homework help USA services to the students of the USA.