+865 Find the sum of all integers that satisfy these conditions:\( |x|+1>7\text{ and }|x+1|\le7. \)
+1094 The answer should be 0: here is why.
Here is a question for you to think about: Is the absolute value just for positive integers, or for both sides of 0?
In other words, if one number works, then it's negation will to, since the absolute value will be the same.
Therefore, if you add all those 0s up, you will get 0.
(If I'm wrong about this, please let me know!)
+1094 Oh! Okay I see. So, the integers MUST be negative for this to work out, or else they will not make any sense. So, we should find the range of both equations and use the overlap.
SO...
The range of |x| + 1 > 7 is (-inf, -6) U (6, inf)
The range of |x+1| <= 7 is [-8, 6].
Therefore, the only values that work are -8 and -7. So, the answer would be -15.
