$|x-1|<\frac{1}{10}$ -এর জন্য নিচের কোনটি সত্য?

$|x-1|<\frac{1}{10}$ $\Rightarrow-\frac{1}{10}<x-1<\frac{1}{10}$ $\Rightarrow-\frac{1}{10}+1<x<\frac{1}{10}+1$ $\Rightarrow \frac{9}{10}$ $<x<\frac{11}{10}$ $\Rightarrow \frac{81}{100}$ $<x^{2}<\frac{121}{100}$ $\Rightarrow-\frac{-19}{100}$ $<x^{2}-1<\frac{21}{100}$ $\Rightarrow \frac{-21}{100}<x^{2}-1$ $<\frac{21}{100}$ $\Rightarrow\left|x^{2}-1\right|<\frac{21}{100}$ $\left[\begin{array}{c}-19>-21 \\-\frac{19}{100}>-\frac{21}{100}\end{array}\right]$