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 .
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Part 1
The minimum speed limit is
enter your response here mi/hr.
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.
To find the minimum speed limit, we need to solve the inequality |S - 54.5 | < 15.5.
Let's break this down into two separate inequalities:
1. S - 54.5 < 15.5
2. -(S - 54.5) < 15.5
Solving the first inequality:
S - 54.5 < 15.5
S < 15.5 + 54.5
S < 70
Solving the second inequality:
-(S - 54.5) < 15.5
-S + 54.5 < 15.5
-S < 15.5 - 54.5
-S < -39
S > 39
Therefore, the minimum speed limit is 39 mph.
To find the minimum speed limit, we need to solve the absolute value equation |S - 54.5| < 15.5.
To solve this equation, we need to consider two cases: when S - 54.5 is positive and when it is negative.
Case 1: S - 54.5 > 0 (Positive Case)
In this case, we have S - 54.5 < 15.5. We can solve this inequality by adding 54.5 to both sides:
S - 54.5 + 54.5 < 15.5 + 54.5
S < 70
Therefore, in this case, the speed limit S is less than 70 mph.
Case 2: S - 54.5 < 0 (Negative Case)
In this case, we have -(S - 54.5) < 15.5. We can solve this inequality by multiplying both sides by -1, which flips the inequality sign:
-(S - 54.5) < 15.5 * -1
S - 54.5 > -15.5
S > 39
Therefore, in this case, the speed limit S is greater than 39 mph.
So, the minimum speed limit is 39 mph.
Please note that the maximum speed limit can be found using the same method, but with the inequality |S - 54.5| < 15.5 reversed.