LINEAR EQUATIONS
Algebra
Exponential equations are those in which the unknown appears in the exponent. For example,
e-2.7x = 290 is an exponential equation. Exponential equations can be of any degree.
The basic principle used in solving any algebraic equation is: any operation performed on one
side of an equation must also be performed on the other side for the equation to remain true.
This one principle is used to solve all types of equations.
There are four axioms used in solving equations:
Axiom 1.
If the same quantity is added to both sides of an
equation, the resulting equation is still true.
Axiom 2.
If the same quantity is subtracted from both sides of
an equation, the resulting equation is still true.
Axiom 3.
If both sides of an equation are multiplied by the
same quantity, the resulting equation is still true.
Axiom 4.
If both sides of an equation are divided by the same
quantity, except 0, the resulting equation is still true.
Axiom 1 is called the addition axiom; Axiom 2, the subtraction axiom; Axiom 3, the
multiplication axiom; and Axiom 4, the division axiom. These four axioms can be visualized by
the balancing of a scale. If the scale is initially balanced, it will remain balanced if the same
weight is added to both sides, if the same weight is removed from both sides, if the weights on
both sides are increased by the same factor, or if the weights on both sides are decreased by the
same factor.
Linear Equations
These four axioms are used to solve linear equations with three steps:
Step 1.
Using the addition and subtraction axioms, Axioms
1 and 2, eliminate all terms with no unknowns from
the left-hand side of the equation and eliminate all
terms with the unknowns from the right-hand side
of the equation.
Step 2.
Using the multiplication and division axioms,
Axioms 3 and 4, eliminate the coefficient from the
unknowns on the left-hand side of the equation.
MA-02
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