Final answer:
For the equation |a-b| = |a| - |b| to be true when b does not equal 0, a must be the negative of b (a = -b). This implies that the positive a is paired with a negative b, fulfilling the properties of absolute values in this context.
Step-by-step explanation:
If b does not equal 0, and |a-b| = |a| - |b|, to determine the relationship between a and b, we need to analyze the properties of absolute values. The equation |a-b| = |a| - |b| can hold true in a situation where both a and b are nonnegative and a is greater than or equal to b. However, the given equation implies that a and b cannot be both positive, as the absolute difference would not result in a subtraction of their absolute values but rather their sum in absolute terms.
Therefore, for the given equation to be true, a must be nonnegative, and b must be nonpositive (since |b| is being subtracted). This implies that a must be a nonnegative number and greater than or equal to b, but since b is not positive, a cannot be equal to b, eliminating options A and B. The correct answer is a scenario where a is positive, and b is its negative counterpart, making a equal to the negative of b (a = -b). As such, we can deduce that a = -b from the given equation, and the answer is D) a = -b.