Question 4

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

The expression |7 - 5| simplifies to 2, and the expression |5 - 7| also simplifies to 2, making them equal.

A) |7| + |-5|

This option evaluates to |7| + |-5|, which is 7 + 5 = 12. This is incorrect as it does not equal 2, the value of |7 - 5|.

B) |5| - |7|

Calculating this gives |5| - |7|, which simplifies to 5 - 7 = -2. The absolute value of -2 is 2, but this does not represent the same expression as |7 - 5| and is not equal to it.

C) |5 - 7|

This option evaluates to |5 - 7|, which simplifies to | -2 |, yielding a value of 2. This is correct as it matches the value of |7 - 5|.

D) |-7 + (-5)|

This option simplifies to |-7 - 5|, resulting in |-12|, which equals 12. This is incorrect since it does not equal 2.

Conclusion

The correct answer is C) |5 - 7|, as both |7 - 5| and |5 - 7| evaluate to the same numerical value of 2. The other options either yield different values or do not represent the same calculation, confirming that C is the only correct choice.