What are the solutions of the following equation? 5∣x+6∣+8=−6∣x+6∣+8

So think of |x+6| as a single object.  Move the -6|x+6| to the left side and move the 8 to the right side to get 11|x+6| = 0.  Then divide both sides by 11 to get |x+6| = 0 and in this instance the || can be dropped because +0 and -0 are the same.  so x + 6 = 0 or x=-6

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