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4 + x = -8
4 + x - 4 = -8 - 4
x = -12

Know the reciprocal of the operation used then do the operation on each of the equation. Just like on the example, the operation of 4 (+4, when it's the first term, the positive sign will be hidden.) which is + (addition) will be just uhh -4. subtract 4 to each of the equation.

Sorry, I can't explain it well but I hope it help.
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With "reciprocal", you mean "inverse".  Your explanation can be easily understood :-) If I may add,  it's better to explain this using the property involved (you mentioned addition).  The problem involves Addition Property (apply the "inverse" operation).  Your answer proved to be coming from your brains, and not copied and pasted :-)
Well, thank you. ☺
4 + x = -8
4 + x - 4 = -8 - 4
x = -12