For how many integer values of x, is |x – 8| + |5 – x| > |x + 7|?
(A) 1
(B) 3
(C) 5
(D) 7
(E) Infinite
You need to check for 4 ranges as the problem has 3 transition points and you will end up with x \in (-\infty,2) \cup(20,\infty) Thus, ans will be E
If you want to learn more about it https://gmatclub.com/forum/inequalities-made-easy-206653.html
I believe that the quickest way to check would be to plug in numbers. x= 1 works. If you wanted to check for E just plug in an x that is not offered and see if the equation still holds.
Ex: x=100
|100-8|+|5-100|>|100+7|
92+95>107