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?
options:
$x - 55 = 4.2$
$x + 55 = -4.2$
$x - 55 = -4.2$
$x + 55 = 4.2$

Explanation:

Step1: Recall absolute value equation

The absolute value equation \(|x - a| = b\) (where \(b\geq0\)) means \(x - a = b\) or \(x - a=-b\). Here, the equation is \(|x - 55| = 4.2\), so it splits into two cases: \(x - 55 = 4.2\) and \(x - 55=- 4.2\).

Step2: Determine maximum speed case

To find the maximum safe speed, we solve for \(x\) in the case that gives the larger value of \(x\). Solving \(x - 55 = 4.2\) gives \(x=55 + 4.2=59.2\), and solving \(x - 55=-4.2\) gives \(x = 55-4.2 = 50.8\). So the equation for the maximum speed is \(x - 55 = 4.2\).

Answer:

\(x - 55 = 4.2\)