Explanation:
an equation means that whatever is on one side of the "=" sign is truly equal to whatever is on the other side.
it is like a balance.
you can change the content on one side of the balance, but then you have to make the same change on the other side of the balance. otherwise the balanced relation between both sides is destroyed. and it is no longer an equation.
for the same reason, you can perform any mathematical operation on an equation, as long as you do it simultaneously on both sides.
all these equations are equations with one variable.
so, if we find a way to bring all terms with the variable to one side, and everything else (typically constant numbers) to the other side, while still maintaining the equation relation, then we can solve this by saying "this is only an equation, if the variable has this is that value".
and that is the whole trick.
so, for e.g. t + 3 = 5, how can we get only the variable on one side ? well, the "+ 3" is disturbing, so we subtract 3.
and to keep the balance, we need to subtract 3 on both sides.
that gives us then
t + 3 - 3 = 5 - 3
t = 2
and boom ! the equation has solved itself right in front of our eyes.
and the same thing for all the other equations.
find what is the disturbing additional term on the side of the variable, then get rid of it (and repeat that exact action on the other side) and see what is left on the other side. and you have solved the equation.
that works in every direction like
n + 22 = 5
n + 22 - 22 = 5 - 22
n = -17
12.5 = 7.4 + z
12.5 - 7.4 = 7.4 - 7.4 + z
5.1 = z or
z = 5.1
remember, it is an equation like a balance. you can switch the balance bowls from left to right and right to left, and still they are in balance.