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# Section P7 Lecture Notes - Equations

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Section P7 Equations Solving Linear Equations in One Variable Example Solve the equation 2 3x 5 5 x 1 x Linear Equations with Fractions Solving with Fractions Example Solve for x x 1 3 2x 1 3 2 12 Example Solve for x x 3 x 1 x 2 5 2 5 Rational Equations A rational equation is an equation containing one or more rational expressions Notice how the variables appear in the denominator in rational equations and the previous examples Linear Equations with Fractions only had variables in the numerator Solving Rational Equations Example Solve the Rational Equation 3 4 1 2 x 2 x 4 x 2 Example 5 2 1 Solve the Rational Equation x 3 x 2 Example 3 2 Solve the Rational Equation 2 6 x 1 x 1 Solving a Formula for One of Its Variables A Prt P A Prt P A P rt 1 A P or rt 1 A P rt 1 Example Solve for l in the formula for the Perimeter of a rectangle Example 1 Solve for b in the formula for the area of a triangle A bh 2 Equations Involving Absolute Value Example Solve x 5 9 7 Example Solve 2 2 x 7 14 0 Quadratic Equations and Factoring Example Solve the equation 2x 5 3x 4 0 using the Zero Product Principle Example Solve the equation by factoring x 2 3 x 4 0 Example Solve the equation by factoring 2x 2 7 x 4 0 Quadratic Equations and the Square Root Property Example Solve the following problem by the square root property x 4 2 25 Example Solve the following problem by the square root property 4x 2 7 0 Quadratic Equations and Completing the Square Obtaining a Perfect Square Trinomial Start Add 2 1 b 2 Result 2 2 x 6 x 1 g6 9 2 x 2 6 x 9 x 3 2 x 2 4 x 4 x 2 2 2 x 4x 1 g 4 4 2 x 2 20 x 1 g 20 100 2 2 Factored Form 2 x 2 20 x 100 x 10 2 Completing the Square Example Complete the square to solve the following problem x 2 10 x 3 0 Example Complete the square to solve the following problem x 2 8 x 13 0 Example Complete the square to solve the following problem x 2 5 x 10 Quadratic Equations and the Quadratic Formula Example Solve the equation using the quadratic formula x 2 6 x 3 Example Solve

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