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Answer:
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).
