In equation >> 2(m-4) = 5m -7; After we Distribute, why do we add 8 on each side instead of 7 on each side. Secondly, why do we subtract 5m on each side instead of 2m±

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You can do it either way, you'll still get the same answer. It depends on which side you like your m to be on, or which you would rather be negative. 2m-8 = 5m -7 --> -3m = 1 --> m= -(1/3) *This method (+8) gives me an m on the left side but makes the m coefficient negative. 2m-8 = 5m-7 --> -1 = 3m --> -(1/3) = m *This method (+7) keeps our m coefficient positive. I personally like keeping my m-coefficient positive, but whatever you prefer or works better for you is fine.