LINEAR EQUATIONSAlgebraExponential 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 oneside 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 anequation, the resulting equation is still true.Axiom 2. If the same quantity is subtracted from both sides ofan equation, the resulting equation is still true.Axiom 3. If both sides of an equation are multiplied by thesame quantity, the resulting equation is still true.Axiom 4. If both sides of an equation are divided by the samequantity, except 0, the resulting equation is still true.Axiom 1 is called the addition axiom; Axiom 2, the subtraction axiom; Axiom 3, themultiplication axiom; and Axiom 4, the division axiom. These four axioms can be visualized bythe balancing of a scale. If the scale is initially balanced, it will remain balanced if the sameweight is added to both sides, if the same weight is removed from both sides, if the weights onboth sides are increased by the same factor, or if the weights on both sides are decreased by thesame factor.LinearEquationsThese four axioms are used to solve linear equations with three steps:Step 1. Using the addition and subtraction axioms, Axioms1 and 2, eliminate all terms with no unknowns fromthe left-hand side of the equation and eliminate allterms with the unknowns from the right-hand sideof the equation.Step 2. Using the multiplication and division axioms,Axioms 3 and 4, eliminate the coefficient from theunknowns on the left-hand side of the equation.MA-02 Page 6 Rev. 0

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