# Absolute Values and Inequality understanding

1. Jun 21, 2010

### jzapata87

1. The problem statement, all variables and given/known data

I saw this in my real analysis text book and I have been trying to understand how this equation $$\left | x-c \right |< 1$$

you can get this:$$\left | x \right |\leq \left | c \right | + 1$$

2. Relevant equations

I wanted to know what steps made this possible , particularly why it changed from $$< to \leq$$

3. The attempt at a solution
My thinking was that, they did this because it makes no difference as to if you put $$< or \leq$$

Any help is appreciated!
Thanks
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jun 21, 2010

### hikaru1221

$$|x|-|c|\leq |x-c| < 1 \Rightarrow |x|-|c| \leq 1$$
This one is true because of the symbol $$\Rightarrow$$ (or as you said, it makes no difference). Things would be different if it were $$\Leftrightarrow$$.

3. Jun 21, 2010

### Susanne217

You forgot to tell the young man that to understand this problem he also needs to understand two of the three basic norms Homogeneity and Subadditivity