1/2(b+14) = b + 14/2 is like writing (1/2).b + (1/2).14 = b + (14/2)
since / has higher preceddence than + and what's inside the parentheses has higher precedence than anything else, here we can't add b to 14 so we have to expand the expression
b/2 + 7 = b + 7 (we add (-7) on both sides to eliminate 7)
<=> b/2 = b (add (-b) on both sides)
<=> b/2 - b = 0
<=> b(1/2 - 1) = 0
<=> b.(-1/2) = 0 ((-1/2) multiplied by sthing equals 0, if we multiply two numbers and the result is 0 then at least one of the two is equal to 0, since (-1/2) isn't equal to 0 then b=0)
<=> b = 0