**Quote:**

Why are the questions "Is |*x* – 1| < 1 ?" and "Is *x* > 0?" the same?

They are the same under the condition that

*x* – 1 < 0, so that we simplify the absolute value: |

*x* – 1| = 1 –

*x* .

In Statement (2) we show that

*x* < 0 implies

*x* – 1 < 0, which turns "Is |

*x* – 1| < 1?" into "Is

*x* > 0?". The latter contradicts Statement (2),

*x* < 0.

If to speak about an equivalent inequality for |

*x* – 1| < 1 with no additional conditions, then it is

-1 <

*x* – 1 < 1

0<

*x* < 2

In other words its solution is that

*x* must be between 0 and 2.