To solve out linear equations we will make heavy use of the following facts.
1. If a = b then a + c = b + c for any c. All it is saying that we can add number, c, to both sides of the equation & not change the equation.
2. If a = b then a - c = b - c for any c. As along with the last property we can subtract a number, c, from both of the sides of an equation.
3. If a = b then ac = bc for any c. Similar to addition & subtraction we can multiply both of sides of equation through a number, c, without varying the equation.
4. If a= b then a/ c = b/c for any non-zero c. We can divide both of the sides of an equation by a non-zero number, c, without varying the equation.
These facts make the basis of almost all the solving techniques which we'll be looking at in this section hence it's very important that you know them and don't forget regarding them. One way to think of these rules is the like as. What we do with one side of an equation we need to do to the other side of the equation. If you recall that then you will always get these facts accurate.
In this section we will be solving linear equations & there is a nice easy procedure for solving linear equations. Let's first summarize the procedure and then we will work some instance.