Compound Inequality Solver
How It Works
This compound inequality solver uses established formulas to provide accurate results.
The basic rule:
- AND: a < cx < b → a/c < x < b/c (if c > 0)
- OR: cx < a OR cx > b
- Flip inequalities when dividing by a negative
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is a compound inequality?
A compound inequality combines two inequalities. An AND compound inequality (intersection) requires both to be true simultaneously. An OR compound inequality (union) requires at least one to be true.
What is the difference between AND and OR?
AND narrows the solution — x must satisfy both conditions (intersection). OR broadens it — x can satisfy either condition (union). AND typically gives an interval like (a,b). OR gives two rays going in opposite directions.
How do I graph a compound inequality?
For AND: shade the overlap of both solution regions on the number line. For OR: shade everything covered by either region. Use open circles for < or > and closed circles for ≤ or ≥.