1c)+Solving+liner+equations,+including+those+with+fractions

 "Linear" equations are equations with just a plain old variable  like "   //x//   ", rather than something more complicated like   //x//2   or   //x/y//   or square roots or such. Linear equations are the simplest equations that you'll deal with. To solve it, you need to get "x" by itself on one side of the equal sign, and a number on the other side.

 Take a look at this equation: X + 3 = 6

In order to get "X" by itself, you will need to subtract 3 from both sides. X + 3-3 = 6-3  X = 3

 Since the // x  // is divided by   5  , I'll want to multiply both sides by   5  <span style="color: rgb(0, 0, 0);"> : <span style="color: rgb(0, 0, 0);"> Then the solution is <span style="color: rgb(128, 0, 128);"> **//x// = –30**  <span style="color: rgb(0, 0, 0);">.
 * **<span style="color: rgb(0, 128, 0);"> Solve //x///5 = <span style="color: rgb(0, 128, 0);"> –6  **

for a more in-depth description of the problem, click [|here] <span style="color: rgb(0, 0, 0);"> <span style="color: rgb(0, 0, 0);"> <span style="color: rgb(0, 0, 0);"> In the above solution (displayed in the animation), I multiplied by <span style="color: rgb(0, 0, 0);"> 5  <span style="color: rgb(0, 0, 0);"> on the right-hand side of the equation, and by  <span style="color: rgb(0, 0, 0);"> 5/1  <span style="color: rgb(0, 0, 0);"> on the left-hand side. Since <span style="color: rgb(0, 0, 0);"> 5 = 5/1  <span style="color: rgb(0, 0, 0);">, this was a legitimate thing to do; I was being "fair" and doing the same thing to both sides of the equation. But why did I do it? Because it is often easier to keep track of what you're doing, when working with fractions, if all the numbers involved are in fractional form. Since I was needing to cancel a <span style="color: rgb(0, 0, 0);"> 1/5  <span style="color: rgb(0, 0, 0);"> on the left-hand side, it was useful to multiply by  <span style="color: rgb(0, 0, 0);"> 5  <span style="color: rgb(0, 0, 0);"> in the form  <span style="color: rgb(0, 0, 0);"> 5/1