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      BASICS

      Imagine the following simple arithmetic equation. 1+2=3

      Although it is a stretch in this case, suppose that one does not know one of the numbers ?+2=3

      This states that some unknown number plus 2 equals 3. While this example is simple enough that one could probably determine that the unknown number is 1, again let us pretend that we do not know this. In that case it is convenient to replace the question mark with a letter called a variables. x+2=3

      Doing math with unknown numbers is all that algebra is about! The rest of one’s study of algebra is all about technique, strategy and terminology.

      Before continuing a piece of terminology must be defined. In algebra we define a term as a segment of a mathematical statement separated by an addition, subtraction or equal sign. So in our last equation the x, 2 and 3 are all separate terms.

      Example 1:

      Replace the number in bold as a letter representing an unknown number. Choice of variables can vary. Solutions are included at the end.

      1. 3−2=1

      2. 1+4=5

      3. 2+7=9

      ADDING IN AN UNKNOWN

      Let us return to the previous example and explore how we can tweak it and still maintain a true statement. So first try simply subtracting 2 from the left side.

      1+2=3 (TRUE)

      1+2−2=3

      1=3 (FALSE)

      We took a true statement and corrupted it into a false statement. However we can still save the day by subtracting 2 from the other side as well.

      1+2−2=3−2

      1=1 (TRUE)

      So by subtracting both sides by the same number we maintain the truthfulness of a statement. But also note that by subtracting by 2 the number two previously there dropped out. So the lessons learned are as follows.

      •When one subtracts from one side of an equation, one must do likewise to the other side to maintain a true statement.

      •When one subtracts a number from an equation its like number drops out of the equation.

      To illustrate the point consider the equation x+2=3.

      We will subtract two from both sides, maintaining a true statement x+2−2=3−2.

      Subtracting 2 will eliminate the original two. This gives us x=1.

      So our unknown number is 1 (surprise!) A similar logic exists when one has subtraction

      x−2=3