Find the sum of all integers that satisfy these conditions:\( |x|+1>7\text{ and }|x+1|\le7. \)

AnimalMaster Jul 23, 2020

#1**+8 **

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!)

ilorty Jul 24, 2020

#3**+8 **

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.

ilorty
Jul 24, 2020