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Convert inequalities to interval notation with brackets and parentheses explained
Interval notation is a mathematical shorthand for representing ranges of numbers. It's more concise than writing out inequalities and is widely used in calculus and advanced mathematics.
Interval notation is more concise and is the standard format in calculus, especially when working with domains, ranges, and continuity. It's also easier to read at a glance.
Use parentheses ( ) when the endpoint is NOT included (< or >), and brackets [ ] when the endpoint IS included (≤ or ≥). Think of brackets as "closing the door" on the number.
Infinity is not a number you can reach or include, it's a concept representing unbounded growth. Therefore, we can never "include" infinity, so it always uses parentheses.
Yes! For example, [3, 7) means 3 ≤ x < 7. The left bracket includes 3, while the right parenthesis excludes 7.
Set-builder notation uses set notation with a vertical bar: {x | x < 5}. Interval notation is more compact: (-∞, 5). Both represent the same set of numbers.
All real numbers is written as (-∞, ∞). Both ends use parentheses because infinity is never included.
No solution is represented by the empty set symbol ∅ or by writing "no solution." There's no interval notation for an empty set.
AND inequalities become a single interval: 3 < x < 7 → (3, 7). OR inequalities use the union symbol: x < 2 OR x > 5 → (-∞, 2) ∪ (5, ∞).