Which of the following is equal to |7 - 5|?

Rationale

|5 - 7| is equal to |7 - 5|.

The absolute value of a number represents its distance from zero, regardless of direction. Since |7 - 5| simplifies to |2|, and |5 - 7| simplifies to |-2|, both expressions yield the same result of 2, illustrating the property of absolute values being equal for both orders of subtraction.

A (|7| + |-5|) YOUR ANSWER

This choice equals |7| + |-5| = 7 + 5 = 12. The absolute values of 7 and -5 are added rather than computed as a difference, resulting in a value far greater than |7 - 5|. Therefore, this expression does not represent the same quantity.

B (|5| - |7|) YOUR ANSWER

This option simplifies to |5| - |7| = 5 - 7 = -2. The absolute value of this expression is 2, but it does not reflect the operation of subtraction in the original question, which measures the distance between the two numbers rather than their difference.

D (|-7 + (-5)|) YOUR ANSWER

This choice results in |-7 - 5| = |-12| = 12. This expression calculates the absolute value of the sum of -7 and -5, which does not relate to the subtraction of 5 from 7, thus yielding a value that is not equal to |7 - 5|.

Conclusion

The absolute value operation emphasizes the distance between two numbers, leading to the equality |7 - 5| = |5 - 7|. Among the choices provided, only C) |5 - 7| properly reflects this property, confirming that both expressions yield the same result of 2. The other options do not adhere to the subtraction mechanism and instead yield different values, demonstrating how absolute values can vary depending on the mathematical operation performed.

Which of the following is equal to |7 - 5|?

|5 - 7| is equal to |7 - 5|.

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