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current learning objective: understanding absolute value
question 20
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cities a and b are on the same north - south line. assume that city a is located at the origin. if the distance from city a to city b is at least 100 miles and x represents coordinate_b - coordinate_a, express this using absolute value notation.
distance represented by absolute value notation: enter your answer
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Explanation:

Step1: Recall absolute - value concept

The absolute value of a number represents its distance from 0 on the number line. Here, since city A is at the origin (0) and \(x\) represents the difference between the coordinates of city B and city A, the distance from city A to city B is \(|x|\).

Step2: Set up the inequality

We are given that the distance from city A to city B is at least 100 miles. In mathematical terms, this means the distance is greater than or equal to 100. So, \(|x|\geq100\).

Answer:

\(|x|\geq100\)