Given that |d - 9| = 2d and we need to find the value of d

Let's solve this using two methods

Method 1: Substitution

Now LHS (Left Hand Side) = Absolute value of a number => it can never be negative
and RHS (Right Hand Side) = 2d
=> negative values of d cannot satisfy this as LHS will be non-negative and RHS will become negative

So, options A and B are out.
Now, let's substitute the value of d from choices C,D,E and see which one satisfies the equation

(C) 1. Put d=1 in |d - 9| = 2d and see if satisfies or not
=> | -1 -9 | = |-10| = 10 \(\neq\) 2*-1 = -2 => NOT POSSIBLE

(D) 3. Put d=3 in |d - 9| = 2d and see if satisfies or not
=> | 3 -9 | = |-6| = 6 = 2*3 = 6 => POSSIBLE

(E) 9. Put d=9 in |d - 9| = 2d and see if satisfies or not
=> | 9 -9 | = |0| = 0 \(\neq\) 2*9 = 18 => NOT POSSIBLE

Method 2: Algebra

|d - 9| = 2d
=> d-9 = 2d or d-9 = -2d
=> 2d-d = -9 or d+2d = 9
=> d = -9 or 3d = 9 or d = \(\frac{9}{3}\) = 3
=> d = -9 or d = 3

If we substitute these values of d back in |d-9| = 2d then we will see that d=-9 does not satisfy the equation
=> d = 3

So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Absolute Values