Remark
You have given the second best answer. Your answer is |x|<1. You should have open circles at 1 and - 1.
Solution
I have enclosed a graph that is not a number line. You could confine yourself to a number line just by tracing out the blue solution (which is the answer you want)
The red solution is what you did.
The blue solution does not include x = 1 nor does it include x = - 1. The number line would show 1 < x < ∞ and -∞ < x < -1