For a certain number d, the expression |2d − 25| is equal to 7. What is the sum of all possible values of d?
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Answer & Explanation
Correct answer
D
An absolute-value equation |2d − 25| = 7 means the inside expression is 7 units from 0 in either direction, so split it into two cases and solve each, then divide by 2 to get d. Case 1 (positive): 2d − 25 = 7, so 2d = 32 and d = 16. Case 2 (negative): 2d − 25 = −7, so 2d = 18 and d = 9. Both values are valid, so the sum of all possible values of d is 16 + 9 = 25, choice (D).
A quick check: for |2d − 25| = 7 the two solutions are symmetric about the value that makes the inside zero, namely d = 12.5, so they must average 12.5 and sum to 25. That confirms the answer without re-solving.
Why the distractors are tempting: (C) 16 keeps only the positive case and (B) 9 keeps only the negative case, the classic slip of dropping one of the two cases. (A) 7 comes from a sign error while isolating d in the negative case (reading d as −9 instead of 9), then summing 16 + (−9). (E) 50 comes from correctly getting 2d = 32 and 2d = 18 but summing those before dividing by 2, so the coefficient on d is never cleared.