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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, −4]

Solution

From -17<3x+10<=-2: -9<x<=-4. From -22<=5x+13<=3: -7<=x<=-2. From -19<=2x-9<=-3: -5<=x<=3. The common solution is [-5,-4].

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