1-20. BASIC ALGEBRAIC PRINCIPLES
a. Algebra is the branch of mathematics used to analyze the relationship of
numbers and concepts with the use of formulas and equations. Algebra is used to find
the value of an unknown factor that is related to known factors. The unknown factor is
usually given the value of "X."
For example: Five times some unknown number is equal to 20. To set this
up as an equation with the unknown factor being X:
5 (X) = 20
b. If two quantities are equal, you may perform identical mathematical functions
to both sides of the equal sign without changing the fact that both sides are equal. If the
factors on one side of the equal sign are multiplied or divided by a number and the
same operation is done to the other side, the resulting factors will be equal. To solve for
X, the X must be isolated on one side of the equal sign. This may usually be
accomplished by dividing both sides by the number in front of X. This number is called
the coefficient of X.
The 5's above and below the line on the left side of the equal sign cancel
X = 20
c. In general, X can be found by dividing the coefficient of X into the number on
the opposite side of the equal sign.