QuestionThe stratosphere is the layer of the Earth’s atmosphere that is more than 10 kilometers (km) and less than 50 km above the Earth’s surface. Which of the following inequalities describes all possible heights x, in km, above the Earth’s surface that are in the stratosphere? A) x + 10 < 50 B) x − 10 < 50 C) x + 30 < 20 D) x − 30 < 20 AnswerThe question states that the stratosphere is the layer of the Earth’s atmosphere that is greater than 10 km and less than 50 km above the Earth’s surface. Thus, the possible heights x, in km, above the Earth’s surface that are in the stratosphere are given by the inequality 10 < x < 50.
To answer the question, you need to find an absolute value inequality that is equivalent to 10 < x < 50. The inequality 10 < x < 50 describes the open interval (10, 50). To describe an interval with an absolute value inequality, use the midpoint and the size of the interval. The midpoint of (10, 50) is 10 + 50 — = 30. Then observe that 2 the interval (10, 50) consists of all points that are within 20 of the midpoint. That is, (10, 50) consists of x, whose distance from 30 on the number line is less than 20. The distance between x and 30 on the number line is x − 30. Therefore, the possible values of x are described by x − 30 < 20, which is choice D.
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