1. Equations www.themegallery.com 33 22 11 Terminology Steps for Solving Examples

2. Terms TerminologyDefinitionExample Equation in xA statement of equality involving one variable, x Solution or Root of an equation in x A number b that yields a true statement when substituted for x 5 is a solution for x 2 -5=4x 5 2 -5=4(5) 25-5=20 20=20 A number b satisfies an equation in x b is the solution of the equation 5 is a solution for x 2 -5=4x Equivalent equationsEquations that have exactly the same solutions (solving for x) 2x+1=6x+3, -1/2 satisfies both sides 2 www.themegallery.com

3. Terms (cont.) TerminologyDefinitionExample Solve an equation in x Find all solutions of the equation To solve (x+3)(X-5)=0, set each factor equal to zero: x+3=0, x-5=0, obtaining the solutions -3 and 5 Linear Equation in xAn equation that can be written in the form ax + b = 0 4x + 5 = 0 3 www.themegallery.com

4. Steps for Solving  1. Determine the lcd of the rational expressions  2. Find the values of the variable that make the lcd equal to zero. These are NOT solutions!  3. Multiply Each Term of the equation by the lcd  4. Simplify! Simplify! Simplify!  5. Factor if necessary  6. Solve for the given variable 4 www.themegallery.com

5. Examples  Solve the equation 6x – 7 + 2x + 5 5

6. More Examples  Solve the equation (8x – 2)(3x-4) = (4x+3)(6x – 1) 6 www.themegallery.com

7. Even More Examples  Solve the equation 7 www.themegallery.com

8. Even More Examples (cont.)  CHECK YOUR WORK!  Not all problems have a solution  You can follow all of the steps perfectly and still have no valid solution 8 www.themegallery.com

9. Practice Problems  Page 66 Problems 1-30 9 www.themegallery.com