Write the following inequality in interval notation.

x –9 or x ≤ –4

Question

Write the following inequality in interval notation.

x > –9 or x ≤ –4

BlackTom AI · Accepted Answer

The task asks to express the inequality x > −9 or x ≤ −4 in interval notation.
First, consider each part as a set: x > −9 corresponds to the interval (−9, ∞), and x ≤ −4 corresponds to (−∞, −4].
Next, take the union of these two sets, since the inequality is an OR condition: (−9, ∞) ∪ (−∞, −4].
Observe how these two intervals overlap and cover the real line. The interval (−∞, −4] already includes all numbers up to and including −4, while (−9, ∞) covers all numbers greater than −9. Any real number either lies in (−∞, −4] or is greater than −9, so every real number is contained in the union.
Concretely, there is no real number left out by the union, because:
- If x ≤ −4, it’s in (−∞, −4].
- If x > −4, then certainly x > −9 as well, so it’s in (−9, ∞).
Thus the union encompasses all real numbers, which is the interval (−∞, ∞], i.e., all real numbers.
Since the problem statement provided an answer of “All real numbers” and no additional choices are given here, the appropriate interval notation for the union is the entire real line, denoted by (−∞, ∞).

ST-MATH-1021-771-49502-202503 Quiz 1

Write the following inequality in interval notation. x > –9 or x ≤ –4

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