Solving Linear Equations
A linear equation in one variable is any equation that can be
written in the form ax + b = 0 (a and b are real numbers and a0). A linear equation has exactly one solution.
STRATEGY FOR SOLVING LINEAR EQUATIONS:
USE ONE OR MORE OF THE FOLLOWING STEPS.
1. Remove symbols of grouping, combine like terms, or reduce
fractions on one or both sides of of the equation.
2. Add (or subtract) the same quantity to both sides of the
equation.
3. Multiply (or divide) both sides of the equation by the same
nonzero quantity.
4. Interchange the two sides of the equation.
Examole 1
5X  10 = 0 add 10 to both sides
5X = 10 divide both sides by 5
X = 2
Example 2
6(X  1) + 4 = 3(7X + 1) remove parenthesis
6X  6 + 4 = 21X + 3 simplify
6X  2 = 21X + 3 add 2 to both sides
6X = 21X + 5 subtract 21X
15X = 5 divide by 15 X
X =5/15 reduce fraction
1/3
SOLVING AN EQUATION INVOLVING FRACTIONAL EXPRESSIONS:
Find the least common denominator of all terms in the equation
and multiply every term by this LCD. This procedure clears the
equation of fractions.
x = 2 is a false solution since it will cause you to have a
zero denominator. Therefore, there is no solution to this
equation.
