|6-4| - |3-8| = ?
A. -7
B. -3
C. 3
D. 7
E. 21
Answer (2)
First, evaluate the expressions inside the absolute values: 6 − 4 = 2 and 3 − 8 = − 5 .
Then, take the absolute values: ∣2∣ = 2 and ∣ − 5∣ = 5 .
Finally, subtract the absolute values: 2 − 5 = − 3 .
The result is − 3 .
Explanation
Initial Analysis We are asked to evaluate the expression ∣6 − 4∣ − ∣3 − 8∣ . Let's break this down step by step. First, we need to evaluate the expressions inside the absolute value signs.
Calculating Inside Absolute Values Next, we calculate the value inside the first absolute value: 6 − 4 = 2 . Then, we calculate the value inside the second absolute value: 3 − 8 = − 5 .
Taking Absolute Values Now, we take the absolute value of each result. The absolute value of 2 is ∣2∣ = 2 . The absolute value of -5 is ∣ − 5∣ = 5 .
Final Subtraction Finally, we subtract the second absolute value from the first: 2 − 5 = − 3 .
Conclusion Therefore, ∣6 − 4∣ − ∣3 − 8∣ = 2 − 5 = − 3 . The answer is -3.
Examples
Absolute values are used in many real-world scenarios, such as calculating distances or errors. For example, if you are measuring the distance between two points, you might get a negative value due to the direction, but the actual distance is always positive, so you take the absolute value. Similarly, in error analysis, the error can be positive or negative, but the magnitude of the error is what matters, so absolute values are used.
The expression ∣6 − 4∣ − ∣3 − 8∣ evaluates to -3 after applying absolute values and performing the subtraction. The correct answer is B. -3.
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