Rationale
|5 - 7| is equal to |7 - 5|.
The absolute value operation removes any negative signs, making the expressions |7 - 5| and |5 - 7| equivalent, both yielding a result of 2. This demonstrates the property of absolute values, where the order of subtraction does not affect the outcome.
A) |7| + |-5|
This expression calculates |7|, which equals 7, and |-5|, which equals 5. Therefore, |7| + |-5| equals 7 + 5 = 12. This value does not relate to |7 - 5|, which equals 2, making this choice incorrect.
B) |5| - |7|
Here, |5| equals 5 and |7| equals 7. Thus, |5| - |7| results in 5 - 7 = -2. Since absolute values cannot yield negative results, this expression does not equal the positive result of |7 - 5|, making it incorrect.
D) |-7 + (-5)|
This expression simplifies to |-12|, which equals 12. The absolute value of the sum of negative numbers does not yield the same result as |7 - 5|, which equals 2. Therefore, this choice is also incorrect.
Conclusion
The equality |7 - 5| = |5 - 7| highlights the property of absolute values where the order of subtraction does not alter the result. Among the provided options, only |5 - 7| correctly simplifies to 2, matching the value of |7 - 5|. The other choices yield different results, reinforcing the unique properties of absolute values in arithmetic operations.
