Question

a road sign shows a vehicles speed as the vehicle passes. complete parts (a) through (c). click the icon to view the road sign. a. the sign blinks for vehicles traveling within 5 miles per hour of the speed limit. write and solve an absolute - value inequality to find the minimum and maximum speeds of an oncoming vehicle that will cause the sign to blink. let x represent the speed of an oncoming vehicle in miles per hour. write an absolute - value inequality to find the minimum and maximum speeds of an oncoming vehicle that will cause the sign to blink. (simplify your answers.)

Explanation:

Step1: Define the speed - limit variable

Let the speed limit be $L$. The difference between the vehicle's speed $x$ and the speed - limit $L$ should be within 5 miles per hour. So, the absolute - value inequality is $|x - L|\leq5$.

Step2: Solve the absolute - value inequality

If $|x - L|\leq5$, then $- 5\leq x - L\leq5$.
Adding $L$ to all parts of the compound inequality:
For the left - hand side: $-5+L\leq x - L+L$, which simplifies to $L - 5\leq x$.
For the right - hand side: $x - L+L\leq5 + L$, which simplifies to $x\leq L + 5$.

Answer:

The absolute - value inequality is $|x - L|\leq5$, and the minimum speed is $L - 5$ miles per hour and the maximum speed is $L + 5$ miles per hour.