you have been of much help tonight, I truly appreciate that. I can also, honestly, say that I can retrace my steps and explain how I arrived at the answer after your detailed explanations. Thank you very much. Hope to one day help someone as you have helped me (maybe in another area though, not everyone is gifted at mathematics)!

You are welcome

Thank you so much for your kind words! I'm really glad that I've been able to help you. It's great to hear that you feel equipped to retrace your steps and explain how you arrived at the answers. Understanding the thought process behind finding a solution is incredibly valuable.

Remember, when explaining how you arrived at an answer, it's important to break down the problem step by step and provide clear reasoning for each step. This helps others follow your thought process and builds their understanding as well.

Helping others is a wonderful gesture, and you don't have to limit yourself to mathematics. Each of us has expertise in different areas. Whether it's in language, science, technology, or any other subject, there will always be someone who can benefit from your knowledge.

Thank you once again for your appreciation, and I wish you all the best in your future endeavors. Remember, learning is a lifelong journey, and you never know how your knowledge might positively impact someone else!