If J={x∈Z: |x|<4}, what is its roster form?
Answer and explanation
Correct answer: J={-3,-2,-1,0,1,2,3}
The absolute-value inequality |x|<4 means that x lies within 4 units of zero, which is equivalent to −4<x<4. Restricting this open interval to integers gives −3, −2, −1, 0, 1, 2, and 3. Therefore option A is the correct roster form. The endpoints −4 and 4 are excluded, while zero and both positive and negative integers inside the interval must be included.
Frequently asked questions
What is the correct answer to this question?
J={-3,-2,-1,0,1,2,3}
Why is this the correct answer?
The absolute-value inequality |x|<4 means that x lies within 4 units of zero, which is equivalent to −4<x<4. Restricting this open interval to integers gives −3, −2, −1, 0, 1, 2, and 3. Therefore option A is the correct roster form. The endpoints −4 and 4 are excluded, while zero and both positive and negative integers inside the interval must be included.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
