# How do you solve m-13.5 =-16.5?

Nov 18, 2016

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.

$m - 13.5 = - 16.5$
$m - 13.5 \textcolor{b l u e}{+ 13.5} = - 16.5 \textcolor{b l u e}{+ 13.5}$

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.

$m \cancel{- 13.5} \cancel{+ 13.5} = - 16.5 + 13.5$

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

$m = - 3$

## 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.