# Thread: how to open an innequality

1. ## how to open an innequality

how they get from this expression

|An+1 - An - L|<e

to

L-e<An+1 - An<L+e

cant understand this transition
??

2. Originally Posted by transgalactic
how they get from this expression

|An+1 - An - L|<e

to

L-e<An+1 - An<L+e

cant understand this transition
??
We know that if $\left|\text{whatever}\right|<\varepsilon$ then it is also true (by definition) that $-\varepsilon<\text{whatever}<\varepsilon$. So applying this concept to your inequality we get $\left|A_{n+1}-A_n-L\right|<\varepsilon\implies -\varepsilon. Adding $L$ to the inequality gives $L-\varepsilon