AnswersMathematics IIIPractice ExamQuestion 27
27
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Practice Exam

Question 27 • Mathematics III

Which of the following gives a single solution of the inequality start absolute value x plus 3 end absolute value minus 2 is less than or equal to 0 and shows a graph that can be used to determine the entire solution set of the inequality?

Answer
A
x is equal to negative 1 Image with description A coordinate plane with a horizontal x-axis labeled from negative 6 to 4 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A V-shaped graph opens upward with its vertex at negative 3 comma 0. A horizontal line passes through 2 on the y-axis, intersecting the V-shaped graph at negative 5 comma 2 and negative 1 comma 2.
B
x is equal to 5 Image with description A coordinate plane with a horizontal x-axis labeled from negative 4 to 6 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A V-shaped graph opens upward with its vertex at 3 comma 0. A horizontal line passes through 2 on the y-axis, intersecting the V-shaped graph at 1 comma 2 and 5 comma 2.
C
x is equal to 0 Image with description A coordinate plane with a horizontal x-axis labeled from negative 6 to 4 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A V-shaped graph opens upward with its vertex at negative 3 comma 0. A horizontal line passes through 2 on the y-axis, intersecting the V-shaped graph at negative 5 comma 2 and negative 1 comma 2.
D
x is equal to 2 Image with description A coordinate plane with a horizontal x-axis labeled from negative 4 to 6 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A V-shaped graph opens upward with its vertex at 3 comma 0. A horizontal line passes through 2 on the y-axis, intersecting the V-shaped graph at 1 comma 2 and 5 comma 2.

Explanation

Add 2 to both sides to get |x + 3| ≤ 2, which means x is between −5 and −1, inclusive. Choice A gives x = −1, a solution, and its graph shows y = |x + 3| intersecting y = 2 at −5 and −1, so it can be used to determine the entire solution set.

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