Question

a road sign shows a vehicles speed as the vehicle passes. complete parts (a) through (c).
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.
|x - 30|≤5
(simplify your answers.)
solve the absolute - value inequality. select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
a. the solution is □≤x≤□
b. the solution is x≥□
c. the solution is x≥□ or x≤□
d. the solution is x≤□
e. the solution is all real numbers.
f. there is no solution.

Explanation:

Step1: Set up the absolute - value inequality

Let the speed limit be assumed as 30 mph (since it seems to be missing in the problem but we see 'x - 30' in the given inequality). The vehicle's speed \(x\) is within 5 miles per hour of the speed limit. The absolute - value inequality is \(|x - 30|\leq5\). This inequality means that the difference between the vehicle's speed \(x\) and the speed limit of 30 mph is at most 5 mph.

Step2: Solve the absolute - value inequality

If \(|x - 30|\leq5\), then \(- 5\leq x - 30\leq5\).
Add 30 to all parts of the compound inequality: \(-5+30\leq x-30 + 30\leq5 + 30\).
\(25\leq x\leq35\).

Answer:

A. The solution is \(25\leq x\leq35\)