Presentation on theme: "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."— Presentation transcript:
1 1.1 Linear EquationsA linear equation in one variable is equivalent to an equation of the formTo solve an equation means to find all the solutions of the equation.
2 Equivalent EquationsTwo 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.