The lawful speeds S on an interstate highway satisfy |S - 54.5 | < 15.5. Find the maximum and minimum speed limits by solving the absolute value equation .

Question

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Part 1
The minimum speed limit is
  
enter your response here ​mi/hr.

Answer 1

To find the minimum speed limit, we need to solve the equation: |S - 54.5 | = 15.5 for S.

Let's consider both cases for the absolute value expression:
1) S - 54.5 = 15.5
2) -(S - 54.5) = 15.5

Case 1:
S - 54.5 = 15.5
S = 15.5 + 54.5
S = 70

Case 2:
-(S - 54.5) = 15.5
-S + 54.5 = 15.5
-S = 15.5 - 54.5
-S = -39
S = 39 (multiplying both sides by -1)

So the minimum speed limit is 39 mi/hr.