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Absolute Value Equations Solve for x and explain your reasoning: 1. x 2 2. x 0 3. x 1 4. x x Since the absolute value of x can either be positive or negative, we must solve for both the positive and negative solutions of x in an absolute value equation. Ex: x2 5 x2 5 x 2 5 +2 +2 +2 +2 X=7 x = -3 {x: x = 7, -3} Try it! 1. x 4 3 2. 9 x 4 5. 2 x 6 14 6. 3x 4 7 Process: 1. Remove the absolute value sign. 2. Solve for the positive solution. 3. Solve for the negative solution. 3. 6 x 9 4. x 12 8 ISOLATING ABSOLUTE VALUE EXPRESSIONS Just like solving for x, we need to isolate the entire absolute value expression before we can solve. Ex: 2x 7 5 4 +5 +5 2x 7 9 2x – 7 = 9 +7 +7 2x = 16 2 2 X=8 2x – 7 = -9 +7 +7 2x = -2 2 2 x = -1 Check by plugging each solution back into your original equation. Examples: 1. 6 x 1 9 2. x 17 9 1 3. 7 4 x 12 4. 3x 2 2 5 5. 4 x 3 4 8 6. 3 2 x 9 10 7. 6 x 5 9 8. 4 5x 8 15 9. 7 3x 10 4 10. 2 3x 7 2 4 Homework: Workbook p. 64, 26-49 EVEN ***EXTRA PRACTICE!*** 1. x 9 4 2. x 7 16 3. 2 x 4 6 9 4. 4 x 10 14 5. 10 3x 1 24 6. 2 x 9 15 36 7. 2 x 1 1 9 2 8. 3 x 1 5 17 2 9. 3 4 x 9 2 6