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# 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 a 0). 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.