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Determine the set of x-values that satisfy all of the following inequalities at the same time: −17 < 3x + 10 ≤ −2; −22 ≤ 5x + 13 ≤ 3; and −19 ≤ 2x − 9 ≤ −3.

1. (−5, −4]
2. [−5, −4]
3. [−5, −3)
4. (−5, −3)

Correct answer: [−5, −3)

Solution

The correct option [−5, −3) represents the range of x-values that satisfy all three inequalities simultaneously, including -5 but not -3, ensuring that both the lower and upper bounds are respected according to the conditions given.

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