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Same approach : it's better to plug 2 values mentally with the respect of abs always positive (or 0) than to solve the original equation (saving energy... 4 hours is long)

If |d-9| = 2d, then d= (A) -9 (B) -3 (C) 1 (D) 3 (E) 9

You can approach this problem in several ways. For example: given |d-9| = 2d --> as LHS (|d-9|) is an absolute value then it's non-negative so RHS (2d or simply d) must also be non-negative thus answer choices A and B are out. Next you can quickly substitute the values to see that d=3 satisfies given inequality: |3-9|=|-6|=6=2*3.

Or you can try algebraic approach and expand |d-9| for 2 ranges: If 0\leq{d}\leq{9} then -(d-9)=2d --> d=3 --> you have an answer D right away; Just to check the second range: If {d}>9 then d-9=2d --> d=-9 --> not a valid solution as d can not be negative (also this value is not in the range we are considering).

Re: If |d-9| = 2d, then d= [#permalink]
02 Oct 2013, 00:35

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