which set of numbers is included in the solution set of the compound inequality?\n{-7, 5, 18, 24, 32}\n{-9…

Answer:

C. {16, 17, 22, 23, 24}

Explanation:

Step1: Analyze the number - line

The number - line shows a closed circle at 15 and 17 (inclusive) and an open circle at 21 (exclusive) with the line extending to the right. This means the compound inequality represents (15\leq x\leq17) or (x > 21).

Step2: Check each set

Set A: ({-7,5,18,24,32})

The numbers (-7) and (5) are not in the solution set as they are less than 15, and 18 is not in the first interval (15\leq x\leq17) and not in the second interval (x > 21).

Set B: ({-9,7,15,22,26})

The numbers (-9) and (7) are less than 15 and not in the solution set.

Set C: ({16,17,22,23,24})

16 and 17 are in the interval (15\leq x\leq17), and 22, 23, 24 are in the interval (x > 21).

Set D: ({18,19,20,21,22})

18, 19, 20 are not in the first interval (15\leq x\leq17) and 21 is not in the solution set since the circle at 21 is open ((x>21)).