Question

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 25≤x≤35. 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. b. another sign blinks when it detects a vehicle traveling within 2 miles per hour of a 35 - miles - per - hour speed limit. write and solve an absolute value inequality to represent the speeds of the vehicles that 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: Set up the absolute - value inequality

The speed limit is 35 miles per hour and the vehicle is within 2 miles per hour of this speed limit. The absolute - value inequality is $|x - 35|\leq2$.

Step2: Solve the absolute - value inequality

If $|x - 35|\leq2$, then $- 2\leq x - 35\leq2$.
Add 35 to all parts of the compound inequality: $-2+35\leq x-35 + 35\leq2 + 35$.
So, $33\leq x\leq37$.

Answer:

The absolute - value inequality is $|x - 35|\leq2$ and the solution is $33\leq x\leq37$.