What is the roster form of L₁ = {x : x ∈ Z, |x + 1| = 3}?
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Answer and explanation
Correct answer: L₁ = {−4, 2}
For an absolute-value equation |x + 1| = 3, there are two possible cases: x + 1 = 3 or x + 1 = −3. These give x = 2 and x = −4, respectively. Both values are integers and satisfy the original equation, so both must be included. Therefore, the roster form is L₁ = {−4, 2}.
Frequently asked questions
What is the correct answer to this question?
L₁ = {−4, 2}
Why is this the correct answer?
For an absolute-value equation |x + 1| = 3, there are two possible cases: x + 1 = 3 or x + 1 = −3. These give x = 2 and x = −4, respectively. Both values are integers and satisfy the original equation, so both must be included. Therefore, the roster form is L₁ = {−4, 2}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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