If x is a real number, then for what values of x is the quantity
- x < 1
- x = 1
- x > 1
- x < -1
- x < -1 or -1 < x << 1
Case 1. (1 – |x|)(1 + x) > 0 if (1 – |x|) > 0 and (1 + x) > 0
(1 – |x|) > 0 and (1 + x) > 0
1 > |x| and x > -1
-1 < x < 1 and x > -1
yields -1 < x < 1
OR
Case 2. (1 – |x|) < 0 and (1 + x) < 0
(1 – |x|) < 0 and (1 + x) < 0
|x| > 1 and x < -1
(x < -1 or x > 1) and x < -1
which yields x < -1
Together these yield x < -1 or -1 < x < 1. The answer is (e).