Question

How do you solve m-13.5 =-16.5?

Answer 1

Isolate `m` by adding `13.5` to both sides.
`m=-3.`

Explanation:

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.