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Compound Inequalities
A compound inequality joins two statements with or or and. Or means union: a number is in the solution set if it works in at least one part. And means intersection: the number must work in both parts at once. A chain such as -2 < x < 5 is a short way to write x > -2 and x < 5, so a chain is AND, not or. Shade both conditions on one number line before you write the answer.
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Compound Inequalities
What is it?
A compound inequality joins two statements with or or and. Or means union: a number is in the solution set if it works in at least one part. And means intersection: the number must work in both parts at once. A chain such as -2 < x < 5 is a short way to write x > -2 and x < 5, so a chain is AND, not or. Shade both conditions on one number line before you write the answer.
In simple words
- A compound inequality joins two statements with or or and.
- Or is union: keep every number that satisfies at least one of the two parts.
- And is intersection: keep only the overlap.
- Read a chain from the middle: -2 < x < 5 says x is greater than -2 and less than 5.
Important terms
or: A compound inequality joins two statements with or or and.
union: Or means union: a number is in the solution set if it works in at least one part.
and: A compound inequality joins two statements with or or and.
intersection: And means intersection: the number must work in both parts at once.
What you should learn
- Explain compound inequalities in clear mathematical language
- Apply the ideas in or means union
- Solve problems involving and means intersection
Examples
- x < 1 or x > 4
- x <= -2 or x >= 5
- x < 0 or x > 0 (all except 0)
OR MEANS UNION
Or is union: keep every number that satisfies at least one of the two parts. For x < 1 or x > 4 the solution set is two separate rays. There is no single interval that covers both. A number such as 2 sits in the gap and belongs to neither set, so it is out.
AND MEANS INTERSECTION
And is intersection: keep only the overlap. For x >= 0 and x < 3 the solution is 0 <= x < 3. The chain -2 < x < 5 means x > -2 and x < 5, so it is AND. Both edges of that chain are open because both symbols are strict. If you wrote -2 <= x <= 5, both edges would be closed.
Recommended for Class 9
Full school-level explanation
A compound inequality joins two statements with or or and. Or means union: a number is in the solution set if it works in at least one part. And means intersection: the number must work in both parts at once. A chain such as -2 < x < 5 is a short way to write x > -2 and x < 5, so a chain is AND, not or. Shade both conditions on one number line before you write the answer.
Union spreads out; intersection overlaps:
What it means
A compound inequality joins two statements with or or and.
Main ideas
1. OR MEANS UNION: Or is union: keep every number that satisfies at least one of the two parts. 2. AND MEANS INTERSECTION: And is intersection: keep only the overlap.
Why it matters
Read a chain from the middle: -2 < x < 5 says x is greater than -2 and less than 5. It does not mean -2 < 5, which is always true and useless. Graph the two walls, then shade only the segment between them for AND, or shade outward for or.
How to answer in an exam
Never replace a chain by or. -2 < x < 5 is intersection, not union. Or produces two regions; and produces the overlap. If the two and-conditions cannot overlap (x > 5 and x < 2), the solution set is empty.
OR MEANS UNION
Or is union: keep every number that satisfies at least one of the two parts. For x < 1 or x > 4 the solution set is two separate rays. There is no single interval that covers both. A number such as 2 sits in the gap and belongs to neither set, so it is out.
Remember
- union
- at least one
- two separate rays
Examples
- x < 1 or x > 4
- x <= -2 or x >= 5
- x < 0 or x > 0 (all except 0)
AND MEANS INTERSECTION
And is intersection: keep only the overlap. For x >= 0 and x < 3 the solution is 0 <= x < 3. The chain -2 < x < 5 means x > -2 and x < 5, so it is AND. Both edges of that chain are open because both symbols are strict. If you wrote -2 <= x <= 5, both edges would be closed.
Remember
- intersection
- overlap
- -2 < x < 5
- AND
Examples
- -2 < x < 5
- 1 <= x <= 4
- x > -1 and x < 2
Remember
- or
- union
- and
- intersection
- -2 < x < 5
- AND
- greater than -2 and less than 5
- AND
How the ideas connect
Read a chain from the middle: -2 < x < 5 says x is greater than -2 and less than 5. It does not mean -2 < 5, which is always true and useless. Graph the two walls, then shade only the segment between them for AND, or shade outward for or.
Deeper understanding
Go beyond memorising Compound Inequalities. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Read a chain from the middle: -2 < x < 5 says x is greater than -2 and less than 5. It does not mean -2 < 5, which is always true and useless. Graph the two walls, then shade only the segment between them for AND, or shade outward for or.
Common mistakes
Exam focus
Core Idea
Key Terms
Main Pattern
Worked Reminder
Exam focus
Quick revision
- or
- union
- and
- intersection
- or: A compound inequality joins two statements with or or and.
- union: Or means union: a number is in the solution set if it works in at least one part.
Never replace a chain by or. -2 < x < 5 is intersection, not union. Or produces two regions; and produces the overlap. If the two and-conditions cannot overlap (x > 5 and x < 2), the solution set is empty.
For long answers on Compound Inequalities: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- or
- union
- and
- intersection
Important formulas
- or
- union
- and
Common exam traps
- Never replace a chain by or.
- -2 < x < 5 is intersection, not union.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Never replace a chain by or.
- Mistake
-2 < x < 5 is intersection, not union.
- Mistake
Do not mix up or means union with and means intersection; use the condition given in the question.
- Mistake
Never replace a chain by or. -2 < x < 5 is intersection, not union. Or produces two regions; and produces the overlap. If the two and-conditions cannot overlap
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
or
union
and
intersection
A compound inequality joins two statements with or or and. Or means union: a number is in the solution set if it works in at least one part. And means intersect
- Definition
- A compound inequality joins two statements with or or and. Or means union: a number is in the solution set if it works in at least one part. And means intersect
- Example
- x < 1 or x > 4
- Critical warning
- Never replace a chain by or.
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Exam Practice
Define
Q1. Define Compound Inequalities.
Explain
Q2. Explain: OR MEANS UNION.
Example
Q3. Give one clear example of Compound Inequalities and say why it fits.
Mistake
Q4. State one common mistake students make about Compound Inequalities.
Exam note
Q5. Write a short exam note on Compound Inequalities: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.