Which is the correct roster form of A={x: x is an integer and |x|<3}?
Answer and explanation
Correct answer: A={-2,-1,0,1,2}
The absolute-value inequality |x|<3 means that x is less than 3 units from zero. Algebraically, it becomes -3<x<3. The integers strictly inside this interval are -2,-1,0,1,2. The endpoints -3 and 3 are excluded, and zero is included because |0|=0<3. Therefore option A gives the complete and correct roster form.
Frequently asked questions
What is the correct answer to this question?
A={-2,-1,0,1,2}
Why is this the correct answer?
The absolute-value inequality |x|<3 means that x is less than 3 units from zero. Algebraically, it becomes -3<x<3. The integers strictly inside this interval are -2,-1,0,1,2. The endpoints -3 and 3 are excluded, and zero is included because |0|=0<3. Therefore option A gives the complete and correct roster form.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Common Questions.
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