I don't understand what the word inextensible mean does it mean if it's pulled outwards the length won't change but if it's pushed inwards it will relaxes ?
Also if what I said is true when can I apply this to a real life problem.
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It sounds like you have the right understanding of inextensible. All real strings (ropes, cables, chains etc.) will stretch to a certain degree when under tension so describing a string inextensible is the sort of idealization common in physics exercises. It allows you to ignore any stretch in the string. For example this would mean that two bodies connected by such a string could have the same displacement and hence the same speed and acceleration which simplifies solutions.
