What is the correct interval form of −3 < x ≤ 0?
Answer and explanation
Correct answer: (−3,0]
The inequality −3 < x excludes −3 because x must be strictly greater than −3. Therefore, the left endpoint uses a parenthesis. The inequality x ≤ 0 includes 0 because equality is permitted, so the right endpoint uses a square bracket. Reading the two endpoint conditions independently gives the interval (−3,0]. This is a half-closed, half-open interval.
Frequently asked questions
What is the correct answer to this question?
(−3,0]
Why is this the correct answer?
The inequality −3 < x excludes −3 because x must be strictly greater than −3. Therefore, the left endpoint uses a parenthesis. The inequality x ≤ 0 includes 0 because equality is permitted, so the right endpoint uses a square bracket. Reading the two endpoint conditions independently gives the interval (−3,0]. This is a half-closed, half-open interval.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Linear Inequalities. Topic: representation on number line.
