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Determine the set of all real values of x that satisfy the inequality |(|x+3|+x)/(x+2) |>1.

1. x∈(-5,-2)∪(-1,∞)
2. x∈(5,2)∪(-1,∞)
3. x∈(-5,2)
4. x∈(-1,∞)

Correct answer: x∈(-5,-2)∪(-1,∞)

Solution

The correct option is right because it accurately captures the intervals where the expression inside the absolute value exceeds 1, considering the behavior of the function across the critical points derived from the inequality.

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