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Author:  Gennadiy [ Wed Aug 04, 2010 9:19 am ]
Post subject:  Re: math: algebra, inequalities

We have three different inequalities in the question statement. Let us solve each one and draw the answer on the number line.

The first inequality is:
|x – 1| < 1
-1 < x – 1 < 1
0 < x < 2

The second inequality is:
(x – 1)² > 1
|x – 1| > 1
x – 1 > 1 or x – 1 < -1
x > 2 or x < 0

The third inequality is
x < 0

We see that shaded area that represents possible values of x for the first inequality doesn't intersect with others. So both statements will give a definite "NO". (You may think of it as if we pick any number from the shaded area on second or third picture it will not be in the shaded area on the first one).

That means that both statements are sufficient on their own.

Furthermore if we had a situation when shaded region for the first inequality partly overlapped with another one then it would mean that corresponding statement is insufficient.

If we had a situation when shaded region for the first inequality completely enclosed another one then it would mean that corresponding statement sufficient (It will give a definite "YES").