The lawful speeds S on an interstate highway satisfy |S-54.5|<=18. Find the maximum and minimum speed limits by solving the absolute value equation |S-54.5|<=18.

Answer 1

To solve the absolute value inequality |S-54.5|<=18, we consider the distance between S-54.5 and 0.

Since |S-54.5| represents the distance between S-54.5 and 0, we can say that -18 <= S-54.5 <= 18.

To find the maximum speed limit, we add 54.5 to both sides of the inequality: -18 + 54.5 <= S-54.5 + 54.5 <= 18 + 54.5.
This simplifies to 36.5 <= S <= 72.

Therefore, the maximum speed limit is 72.

To find the minimum speed limit, we subtract 54.5 from both sides of the inequality: -18 - 54.5 <= S-54.5 - 54.5 <= 18 - 54.5.
This simplifies to -72.5 <= S <= -36.5.

However, speed limits are positive values, so the minimum speed limit is 0.

Therefore, the maximum speed limit is 72 mph and the minimum speed limit is 0 mph.