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This questions seems ackward. I get two scenarios - 9 and 3 and since d has to be +ve D (3) is the answer

If E is the answer then |d -9| = |9 -9| = 0 which is not possible.

What is the source of your question?

This is how I solved : |d-9|=2d

=> d> 0, d-9 =2d ->d = -9 but this contradicts the assumption d>0

=> d<0 , -(d-9 ) = 2d -d+9=2d 3d =9 =>d=3

You're almost there, except you made a small confusion that led to a contradiction by the end of your proof too: you conclude with d=3 when you assumed d<0 to make the calculations

This is because |d-9| = d-9 when d \(\ge\) 9 and 9-d when d \(\le\) 9 (and not 0)

=> d> 0, d-9 =2d ->d = -9 but this contradicts the assumption d>0

=> d<0 , -(d-9 ) = 2d -d+9=2d 3d =9 =>d=3[/quote] You're almost there, except you made a small confusion that led to a contradiction by the end of your proof too: you conclude with d=3 when you assumed d<0 to make the calculations

This is because |d-9| = d-9 when d \(\ge\) 9 and 9-d when d \(\le\) 9 (and not 0)[/quote]