For any non-zero a and b, that satisfy |ab| = ab and |a| = -a, |b – 4| + |ab – b| = A. ab – 4 B. 2b – ab – 4 C. ab + 4 D. ab – 2b + 4 E. 4 – ab
(D) We know that |a| = -a. Since an absolute value must be positive, then -a > 0, which results in a < 0. Considering this fact together with |ab| = ab we reason out that b < 0, because ab > 0 and a < 0. So (b – 4) < 0 as well. Therefore |b – 4|= 4 – b b < 0 and a – 1 < 0 so b(a – 1) > 0 |ab – b| = |b(a – 1)| = b(a – 1).
Summarizing all of the above reasoning we get |b – 4| + |ab – b| = -b + 4 + ab – b = ab – 2b + 4
If you are unable to make sense of the algebra, you can plug in negative numbers for the two values in each of the answer choices to get choice (D). ---------- Explanation is not clear at all.
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