Challenge Problem! Work in your groups to do this problem: 12 x2 x 2x2 4x 6 x2 1 A.5 Methods for Solving Equations Failures are finger posts on the road to achievement. -C. S. Lewis Domain Recall: The domain is the set of all x values for which an expression exists. Ex. Find the domain of the following expression. 3x 2 3x 3 4 x 2 9x 12 Solve vs. Simplify! This is what we did before: 3 𝑥−4 − 2 𝑥 − 1 𝑥 − 2𝑥 + 1 SIMPLIFY This is what we’re doing now: 3 1 7 = + 2 𝑥 − 2 𝑥 − 1 𝑥 − 3𝑥 + 2 SOLVE Solving Rational Equations Recall how to solve the following equation… x 1 1 5x5x 2 3 36 6 Steps for Solving Rational Equations Step 1: Factor all denominators completely. Step 2: Determine the least common multiple. Step 3: Multiply both sides by the LCM (distribute!). Step 4: Solve the new polynomial equation using learned methods. Step 5: Check for any extraneous solutions in the original equation. Solving Rational Equations Solve the equation. 7 3 11 7 1 (x 1)(x 2) (x 1)(x 2) x 2 xx 1 Solving Rational Equations What if we have one a little more tricky?! 5 2 2 3x 1 3x 5x 2 Solving Rational Equations Do with your groups and turn in! Pg 998 #42, 78, 80 Solve or Simplify?? a) c) 3 𝑥−4 − 2 𝑥 − 1 𝑥 − 2𝑥 − 24 𝑥 𝑥+3 −3 − = 𝑥2 − 1 𝑥2 − 𝑥 𝑥2 + 𝑥 b) d) 4(𝑥 − 2) 3 −3 + = 𝑥−3 𝑥 𝑥(𝑥 − 3) 1 1 ℎ 𝑥+ℎ 1 2 − 𝑥2 Homework #6: p.998 #41, 45, 46, 77, 79, 80 A.5 Methods for Solving Equations Failures are finger posts on the road to achievement. -C. S. Lewis Solving Absolute Value Equations What does “absolute value” mean? x 7 What is the meaning of this equation? 2x 3 7 Steps for Solving Absolute Value Equations Step 1: Isolate absolute value on one side of the equation. x a Step 2: Rewrite the equation, removing the absolute value, and plus/minus of the other side of the equation. x a Step 3: Solve each equation for x. xa x a Step 4: Check for any extraneous solutions in the original equation. Solving Absolute Value Equations Solve the following equation for x. 3x 1 9 2x Homework #6: p.998 #41, 45 – 59 odd, 77, 79 A.5 Methods for Solving Equations Failures are finger posts on the road to achievement. -C. S. Lewis