LINEAR EQUATIONS
Algebra
Example:
Solve the equation 4x + 3 = 19 by transposing.
Solution:
Step 1.
Transpose the 3 from the left-hand to the right-hand
side of the equation by changing its sign.
4x
= 19 - 3
4x
= 16
Step 2.
Using Axiom 4, divide both sides of the equation by
4.
4x
4
16
4
x = 4
Step 3.
Check the root.
4(4) + 3 = 16 + 3 = 19
The root checks.
Solving Fractional Equations
A fractional equation is an equation containing a fraction. The fraction can be either a common
fraction or a decimal fraction. The unknowns can occupy any position in the equation. They
may or may not be part of the fraction. If they are part of the fraction, they can be either in the
numerator or the denominator. The following are three examples of fractional equations:
5x
1
2
8
2x
6
3x
9
y
0.67x
1.25y
9
Fractional equations are solved using the same axioms and approach used for other algebraic
equations. However, the initial step is to remove the equation from fractional form. This is done
by determining the lowest common denominator (LCD) for all of the fractions in the equation
and then multiplying both sides of the equation by this common denominator. This will clear
the equation of fractions.
MA-02
Page 10
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