Compound Inequality Calculator
Solve compound inequalities with AND/OR operations
Solve Compound Inequality
AND: Both conditions must be true (intersection)
OR: At least one condition must be true (union)
Frequently Asked Questions
What is a compound inequality?
A compound inequality consists of two inequalities joined by "and" or "or". It describes a range or combination of values that satisfy both or either condition.
How do you solve AND inequalities?
For AND inequalities, find the intersection of solutions. Both conditions must be true. For x > 2 AND x < 5, the solution is 2 < x < 5 or (2, 5).
How do you solve OR inequalities?
For OR inequalities, find the union of solutions. At least one condition must be true. For x < 2 OR x > 5, the solution is (-∞, 2) ∪ (5, ∞).
Can an AND inequality have no solution?
Yes! If the conditions contradict each other, like x > 5 AND x < 2, there's no solution because no number can be both greater than 5 and less than 2.
How do you graph compound inequalities?
For AND, shade the overlapping region. For OR, shade both regions. Use open circles for < or > and closed circles for ≤ or ≥.
What is the difference between AND and intersection?
They're the same! AND means intersection (∩). OR means union (∪). AND narrows the solution set, OR broadens it.