The solution set of the compound inequality is (-∞, 9] ∪ [17, ∞) and the correct graphical representation on the number line can be seen in the first option.
What is a solution set of a compound inequality?
The solution set of a compound inequality is the set of values that intersect between the two inequalities and they satisfy the solution to each individual inequality.
The graph of a compound inequality can be illustrated on the number line.
From the given information, we have:
[tex]\mathbf{-\dfrac{1}{3}x+10 \geq 7}[/tex]---- (1)
x - 10 ≥ 7 ----- (2)
From equation (1), the solution to the inequality is:
- x ≤ 9 and the interval notation can be represented as (-∞, 9]
The solution to the second inequality is:
- x ≥ 17 and the interval notation is [17, ∞)
The solution set of the compound inequality is (-∞, 9] ∪ [17, ∞) and the correct graphical representation on the number line can be seen in the first option.
Learn more about the solution set of a compound inequality here:
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