If |2x +1| = 2 |k - x|, for all values of x, what is the value of |k|?

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  k = -1/2

Step-by-step explanation:

On the right, we can distribute the 2, so we have ...

   |2x +1| = |2k -2x|

We can multiply inside the brackets on the right by -1 with no effect:

  |2x +1| = |-2k +2x|

Comparing the expressions now, we see they are equivalent when ...

  1 = -2k

  k = -1/2

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In the attached graph, the left-side expression is red; the right-side expression is blue dots (when k = -1/2).

[see below]

Step-by-step explanation:

Hope this helps.