The lawful speeds S on an interstate highway satisfy |S-53.5) ≤20.5. Find the maximum and minimum speed limits by solving the absolute value equation |S-53.5)=20.5.

Question

The minimum speed limit is __ mi/hr.

Answer 1

To find the maximum and minimum speed limits, we need to solve the absolute value equation |S-53.5| = 20.5.

When a number is inside absolute value bars, it can either be positive or negative. So we have two cases to consider:

Case 1: S - 53.5 is positive
In this case, |S - 53.5| = S - 53.5. So the equation becomes:
S - 53.5 = 20.5

Solving for S:
S = 20.5 + 53.5
S = 74

So, one possible speed limit is 74 mph.

Case 2: S - 53.5 is negative
In this case, |S - 53.5| = -(S - 53.5) = -S + 53.5. So the equation becomes:
-S + 53.5 = 20.5

To solve for S, we isolate the variable:
-S = 20.5 - 53.5
-S = -33

Multiplying by -1 to get the positive value of S:
S = 33

So, the other possible speed limit is 33 mph.

Therefore, the minimum speed limit is 33 mph.