Compound Inequalities
Two inequalities joined by and or or.
About this topic
A compound inequality joins two inequalities with "and" or "or". An "and" statement like −2 less than x and x at most 5 means both must hold, giving the overlap, a single interval. An "or" statement such as x less than 1 or x greater than 4 gives values that satisfy at least one condition, often two separate pieces.
Solve each part separately, or work on all three sections at once for the combined form, then graph the result on a number line. For −3 less than 2x + 1 at most 9, subtract 1 from all three parts to get −4 less than 2x at most 8, then divide by 2 to get −2 less than x at most 4. Remember to flip the signs if you divide by a negative. These are used to describe ranges like acceptable temperatures or safe weights.
Imagine a roller coaster that admits riders at least 120 cm tall but under 195 cm. That is an "and" condition, 120 at most h and h less than 195. By contrast, a discount for children under 5 or seniors over 65 is an "or" condition with two separate groups. On a number line, "and" is where the shading overlaps, while "or" is the union of the shaded regions.
A common mistake is writing an "or" answer in the chained form, like 4 less than x less than 1, which is impossible. Also, an "and" with no overlap, such as x less than 1 and x greater than 4, has no solution at all.
Key ideas
- AND means both must be true, giving an interval
- OR means either is true
- Write as a < x < b
Quick check
Use cases: where Compound Inequalities helps
- Homework: review the key idea behind Compound Inequalities before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Compound Inequalities without notes.
- Visual learning: play with the interactive lab to see how Compound Inequalities changes when you adjust its inputs.
- Teaching a friend: explain Compound Inequalities in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Compound Inequalities?
Two inequalities joined by and or or.
What will I learn in Compound Inequalities?
AND means both must be true, giving an interval. OR means either is true. Write as a < x < b.
Is Compound Inequalities part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Compound Inequalities lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Compound Inequalities?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.