Linear Inequalities • Topic 3 of 4

Interval Notation

Interval notation is a compact way to write a solution range. Parentheses ( ) mean an endpoint is excluded (strict < or >); square brackets [ ] mean it is included (≤ or ≥). So x > 2 is (2, ∞), and −1 ≤ x < 3 is [−1, 3). Infinity always takes a parenthesis because it is never reached. The smaller number is written first. Converting between inequalities, number lines and interval notation is a quick SAT skill: match each ≤/≥ to a bracket and each </> to a parenthesis.

✅ Solved examples

1. Write x > 5 in interval notation.
Excluded endpoint and unbounded above: (5, ∞).
2. Write −2 ≤ x ≤ 4 in interval notation.
Both endpoints included: [−2, 4].
3. Write x ≤ 3 in interval notation.
Unbounded below, included endpoint: (−∞, 3].
4. Write 0 < x < 6 in interval notation.
Both endpoints excluded: (0, 6).

✏️ Practice — try these, take hints as needed

1. Write x ≥ 1 in interval notation.
Included endpoint → bracket.
Unbounded above → ∞ with parenthesis.
[1, ∞).
[1, ∞).
2. Write −3 < x ≤ 2 in interval notation.
Left strict → parenthesis.
Right inclusive → bracket.
Order low to high.
(−3, 2].
3. Write x < 0 in interval notation.
Unbounded below.
Strict endpoint → parenthesis.
(−∞, 0).
(−∞, 0).
4. Write 4 ≤ x < 10 in interval notation.
Left inclusive → bracket.
Right strict → parenthesis.
[4, 10).
[4, 10).
5. Write the interval (−∞, 5] as an inequality.
Bracket means inclusive.
Unbounded below.
x ≤ 5.
x ≤ 5.

📝 Topic test — 8 questions

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