kvcpk wrote:
Is |x+1|<2?
means is -2 < x+1 < 2
Hello guys,
Let me show you a DIFFERENT way (quicker and safer) to answer this question in the affirmative!
If
a and
b are any two real numbers, the DISTANCE between them (in the real line) is ALWAYS equal to |
a-
b| , to be honest, it is DEFINED this way (check some values for
a and
b to see this is very reasonable!
That understood, once you realize that |x+1| = |x-(-1)| = distance (x, -1), the question is:
Is the distance between
x and the number -1 less than 2 (units of length)? And, of course, (draw a line with the number -1 as a "reference", then -2 and +2 to the left and right.... and verify that) this is equivalent to the question is
x between -1 -2 = -3 and -1 +2 = 1 (both extremities excluded)? Please note that -3 < x < 1 (as a question) is equivalent to the question you put, that is, -2 < x+1 < 2 ?
I called this the "geometric representation of modulus". Very useful, no doubt! I hope you like (and use) it!!
Regards,
Fabio.
