Find the given distances between points P, Q, R, and S on a number line, with coordinates -4, -1, 8, and 12, respectively. See Example 3. d (P, Q)

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Identify the coordinates of points P and Q on the number line. Here, P = -4 and Q = -1.

Recall that the distance between two points on a number line is the absolute value of the difference of their coordinates. The formula is: \(d(P, Q) = |x_Q - x_P|\).

Substitute the coordinates of P and Q into the formula: \(d(P, Q) = |-1 - (-4)|\).

Simplify the expression inside the absolute value: \(-1 - (-4) = -1 + 4\).

Calculate the absolute value to find the distance: \(d(P, Q) = |3|\).

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