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 __ mi/hr.
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.
To find the minimum speed limit, we need to solve the absolute value equation |S-53.5| = 20.5.
We know that the absolute value of a number is equal to the number itself if it is positive and the negation of the number if it is negative. Therefore, we have two cases to consider:
Case 1: S - 53.5 = 20.5 (since the expression inside the absolute value is positive)
S - 53.5 = 20.5
S = 20.5 + 53.5
S = 74
Case 2: -(S - 53.5) = 20.5 (since the expression inside the absolute value is negative)
-S + 53.5 = 20.5
-S = 20.5 - 53.5
-S = -33
S = 33
So, the minimum speed limit is 33 mi/hr.
To find the minimum speed limit, we need to solve the absolute value equation |S-53.5| = 20.5.
First, let's consider the two possible cases:
Case 1: S - 53.5 is positive, i.e., S - 53.5 > 0
In this case, the absolute value equation becomes S - 53.5 = 20.5.
Adding 53.5 to both sides of the equation, we have S = 74.
Case 2: S - 53.5 is negative, i.e., S - 53.5 < 0
In this case, the absolute value equation becomes -(S - 53.5) = 20.5.
Multiplying both sides of the equation by -1, we have S - 53.5 = -20.5.
Adding 53.5 to both sides of the equation, we have S = 33.
Therefore, the maximum speed limit is 74 mi/hr and the minimum speed limit is 33 mi/hr.