How do you solve m-13.5 =-16.5?

We're looking for a value #m# such that when we subtract #13.5# from #m#, we get #-16.5#. Thus, #m# must be #13.5# greater than #-16.5#.

This equation is like a balanced scale. Right now, #m-13.5# is on one side, and #-16.5# is on the other. We are told that these values balance each other. We want to isolate #m#, but to do that, whatever we introduce needs to keep things balanced. If we add something to the left, we have to add it to the right.

#m-13.5=-16.5#
#m-13.5color(blue)( +13.5)=-16.5color(blue)( +13.5)#

Here, we choose to add 13.5 to both sides so that the #-13.5# on the left side will be cancelled off. Remember, add it to both sides, so that the "scale" remains balanced.

#mcancel(-13.5)cancel(+13.5)=-16.5+13.5#

The LHS simplifies to just #m#, which is what we want. Whatever ends up being on the RHS is thus what #m# is equal to.

After adding #-16.5+13.5#, we get

#m=-3#

as our answer.

Footnote:

By adding some value to both sides, we create an equation that contains the same information, but says it in a different way. If we choose what we add (or multiply, or whatever) carefully, the new equation can be more useful. For example here, what we're saying is that if

#m-13.5=-16.5#

is true, then

#m=-3#

is also true, and this is a much more useful form of the same information.