In this video we are going to be working on solving simple equations, by making use of one basic principle.
The main thing to remember when solving equations
is that whatever you do to one side of an equation you must also due to the other side.
As long as we follow this rule we can do as many operations as necessary to solve an equation.
Here we want to solve the equation 7m + 10 is equal to negative 6 minus m.
In order to solve this we first want to have all of the terms involving an "m" on one side of the equation
and all of the terms which are numbers on the other side of the equation.
Here we're going to choose to move the terms containing an "m" to the left side of the equation
and the numbers to the right side.
In order to get rid of the negative m on the right side of the equation
you need to do the opposite operation of subtracting, which means you need to add an m.
Whatever you do to one side of the equation must also be done to the other side,
so you must add m to both sides of the equation.
On the right side m subtract m is equal to 0 so we have eliminated m  from the right side.
Then you want to eliminate the positive 10 from the left side of the equation,
so you need to do the opposite of adding 10 by subtracting 10 from both sides of the equation.
On the left side 10 subtract 10 is equal to 0, so we have eliminated 10 from the left side of the equation.
Then combine like terms on each side of the equation.
On the left side add the coefficients of the m's to get that 7m + m is equal to 8m
and on the right side compute negative 6 subtract 10, which is equal to negative 16.
Now the m, which we are trying to solve for, is being multiplied by eight.
So in order to get the m by itself we need to divide both sides of the equation by eight.
This works nicely because on the left side of the equation 8m / 8 is equal to m, so we finally have "m" by itself.
On the right side of the equation negative 16 / 8 is equal to negative 2.
Thus we have found that the solution to this equation is m equal to negative 2.
Now we remember that in the standard form of a trinomial we have a*x squared plus b*x plus c.
We explain how Archimedes chose pi from perimetrus, meaning perimeter, when determining the circumference of a circle.
But what Archimedes used PI to represent wasn't the constant 3.14159 we know it as today..
