The lawful speeds S on an interstate highway satisfy StartAbsoluteValue Upper S minus 55.5 EndAbsoluteValue less than or equals 20.5

Question

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Find the maximum and minimum speed limits by solving the absolute value equation StartAbsoluteValue Upper S minus 55.5 EndAbsoluteValue equals 20.5
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Question content area bottom
Part 1
The minimum speed limit is 35

​mi/hr.
Part 2
The maximum speed limit is enter your response here

​mi/hr.

Answer 1

To find the maximum and minimum speed limits, we can solve the absolute value equation:

|S - 55.5| = 20.5

To solve for S, we will consider the two cases:

Case 1: S - 55.5 = 20.5

Adding 55.5 to both sides, we have:

S = 76

Case 2: -(S - 55.5) = 20.5

Expanding the equation, we have:

-S + 55.5 = 20.5

Subtracting 55.5 from both sides and multiplying by -1, we get:

S = 35

Therefore, the maximum speed limit is 76 mph and the minimum speed limit is 35 mph.