Question

on certain areas of the highway, drivers can get fined for going under 40 mph or by driving 75 mph or faster. write a compound inequality to model the situation

Explanation:

Step1: Define the variable

Let \( x \) represent the speed of the driver in miles per hour (mph).

Step2: Analyze the first condition

Drivers can get fined for going under 40 mph. This means the speed \( x \) is less than 40, which can be written as \( x < 40 \).

Step3: Analyze the second condition

Drivers can also get fined for driving 75 mph or faster. This means the speed \( x \) is greater than or equal to 75, which can be written as \( x \geq 75 \).

Step4: Combine the two conditions

Since the driver can be fined for either of these two situations (going under 40 mph or 75 mph or faster), we use the "or" connector to combine the two inequalities. So the compound inequality is \( x < 40 \) or \( x \geq 75 \).

Answer:

The compound inequality that models the situation is \( x < 40 \) or \( x \geq 75 \) (or in boxed form, \(\boxed{x < 40 \text{ or } x \geq 75}\))