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
The minimum speed limit is 33ml / h * r
The maximum speed limit is __ mi / h * r
To solve the absolute value equation |S - 53.5| = 20.5, we can set up two separate equations:
1) S - 53.5 = 20.5
S = 74
2) -(S - 53.5) = 20.5
-S + 53.5 = 20.5
S = 33
So, the maximum speed limit is 74 mph and the minimum speed limit is 33 mph.
To solve the absolute value equation |S - 53.5| = 20.5, we need to consider two cases:
Case 1: S - 53.5 ≥ 0
In this case, the equation becomes S - 53.5 = 20.5, and solving for S gives us:
S = 20.5 + 53.5
S = 74
So the maximum speed limit is 74 mph.
Case 2: S - 53.5 < 0
In this case, the equation becomes -(S - 53.5) = 20.5, which simplifies to -S + 53.5 = 20.5. Solving for S gives us:
-S = 20.5 - 53.5
-S = -33
S = 33
So the minimum speed limit is 33 mph.
Therefore, the maximum speed limit is 74 mph and the minimum speed limit is 33 mph.
To solve the absolute value equation |S - 53.5| = 20.5, we need to consider two separate cases:
Case 1: (S - 53.5) = 20.5
Case 1 simplifies to S - 53.5 = 20.5
Adding 53.5 to both sides of the equation, we get:
S = 20.5 + 53.5
S = 74
Case 2: - (S - 53.5) = 20.5
Case 2 simplifies to -S + 53.5 = 20.5
Subtracting 53.5 from both sides of the equation, we get:
-S = 20.5 - 53.5
Simplifying further, we have:
-S = -33
Dividing both sides of the equation by -1, we get:
S = 33
Therefore, the maximum speed limit is 74 mph, and the minimum speed limit is 33 mph.