LINEAR EQUATIONSAlgebraExample:Solve the equation 4x + 3 = 19 by transposing.Solution:Step 1. Transpose the 3 from the left-hand to the right-handside of the equation by changing its sign.4x= 19 - 34x= 16Step 2. Using Axiom 4, divide both sides of the equation by4.4x4164x = 4Step 3. Check the root.4(4) + 3 = 16 + 3 = 19The root checks.SolvingFractionalEquationsA fractional equation is an equation containing a fraction. The fraction can be either a commonfraction or a decimal fraction. The unknowns can occupy any position in the equation. Theymay or may not be part of the fraction. If they are part of the fraction, they can be either in thenumerator or the denominator. The following are three examples of fractional equations:5x1282x63x9y0.67x1.25y9Fractional equations are solved using the same axioms and approach used for other algebraicequations. However, the initial step is to remove the equation from fractional form. This is doneby determining the lowest common denominator (LCD) for all of the fractions in the equationand then multiplying both sides of the equation by this common denominator. This will clearthe equation of fractions.MA-02 Page 10 Rev. 0

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