|x| is a twin in disguise, it really means, if we get rid of the bars, it means -(whatever inside the bars) +(whatever inside the bars)
so, in this case, is just "x", so it means -x and +x, now, if we slap the <1 to it
we end up with
+x < 1 and -x < 1, which can also be written as x > -1
in interval
x < 1 "x" is less than 1, what values are less than 1? anything from 0 to the left, so (-∞, 1) <---- notice, we used that one, but has a parentheses, so, is not part of that group, just there as reference
x > -1 "x" is greater than -1, what values are larger than -1? well, anything to the right of it, or from 0 to the right, or (-1, +∞)