I have this inequality :

$$|g(x)-B|<\frac{|B|}{2}$$ 
$$-\frac{|B|}{2}<g(x)-B<\frac{|B|}{2}$$
$$B-\frac{|B|}{2}<g(x)<B+\frac{|B|}{2}$$

I don't understand how it possible to conclude from the inequality that

$$\frac{|B|}{2}<|g(x)|$$ 

Thanks.