1. 1.1 Linear Equations
A linear equation in one variable is equivalent to an equation of the form
To solve an equation means to find all the solutions of the equation.

2. Equivalent Equations
Two or more equations that have precisely the same solutions are called equivalent equations.
Examples of equivalent equations:

3. Solving a Linear Equation
Solve the equation:
We replace the original equation by succession of equivalent equations.
Add 5 to both sides.
Simplify.
Divide both sides by 3.

4. Solving a Linear Equation Involving Fractions
Multiply both sides by the least common denominator 30.
Be sure to multiply all terms by 30.
Divide out common factors.
Subtract 5x to get the x-terms on the left.
Simplify.
Solve the equation:

5. Solve an Equation Involving Rational Expressions

6. This is the given equation.
Multiply both sides by 5x (LCD).
Be sure to multiply all terms by 5x.
Divide out the common factors.
Simplify.
Subtract 4 from both sides.
Divide both sides by 2.