Question

on the freeway, it is unsafe to drive too slowly or too quickly. the safest driving speeds on the freeway near allans town were scientifically determined to be between the minimum and maximum speeds (in miles per hour) according to the equation |x - 55| = 4.2. which equation can be used to determine the maximum safe driving speed?
○ x - 55 = 4.2
○ x - 55 = -4.2
○ x + 55 = 4.2
○ x + 55 = -4.2

Explanation:

Step1: Recall the absolute value equation property

The absolute value equation \(|A| = B\) (where \(B\geq0\)) is equivalent to \(A = B\) or \(A=-B\). Here, the equation is \(|x - 55|=4.2\), so this is equivalent to \(x - 55 = 4.2\) or \(x - 55=- 4.2\).

Step2: Analyze the meaning of each equation for speed

We want the maximum safe speed. Solving \(x - 55 = 4.2\) will give \(x=55 + 4.2\), which is a larger value (since we are adding 4.2 to 55). Solving \(x - 55=-4.2\) will give \(x = 55-4.2\), which is a smaller value (subtracting 4.2 from 55). The other two options (\(x + 55 = 4.2\) and \(x + 55=-4.2\)) would lead to \(x\) values that are much smaller (since we would be subtracting 55) and don't make sense for maximum speed on a freeway. So the equation to find the maximum safe speed is \(x - 55 = 4.2\).

Answer:

A. \(x - 55 = 4.2\)