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Absolute Value Equations and Inequalities: Solutions and Understanding Checks

Learn how to solve absolute value equations and inequalities step by step with detailed explanations and practice problems. Check your understanding to ensure mastery of the concepts.

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Absolute Value Equations and Inequalities: Solutions and Understanding Checks

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  1. Ch. 1-5 Absolute Value Equations and Inequalities

  2. Ex. 1: Solve | 15 – 3x | = 6 | 15 – 3x | = 6 15 – 3x = 6 15 – 3x = -6 -15 -15 -15 -15 -3x = -9 -3x = -21 x = 7 x = 3

  3. Solve Check understanding 1 p. 33

  4. Ex. 2: 4 – 2|x + 9| = -5 4 – 2|x + 9| = -5 -4 -4 -2|x + 9| = -9

  5. Ex. 3 cont. -9 -9 -9 -9 x = -13.5 x = -4.5

  6. Solve check understanding 2 p. 34

  7. Ex. 3: Solve |3x – 4| = -4x - 1 3x – 4 = -4x – 1 3x – 4 = 4x + 1 -3x -3x +4x +4x 7x – 4 = -1 -4 = x + 1 -1 -1 +4 +4 x = -5 7x = 3

  8. When there is a variable outside of the absolute value, you must check your answers. x = -5 | 3(-5) – 4 | = -4(-5) -1 | -15 – 4 | = 20 - 1 | -19 | = 19 19 = 19 Solution Not a solution

  9. Solve check understanding 3A and 3B, p. 34

  10. Ex. 4: Solve | 2x – 5 | > 3. Graph the solution. 2x – 5 < -3 2x – 5 > 3 +5 +5 +5 +5 2x < 2 2x > 8 x < 1 x > 4

  11. Solve check understanding 4 p. 35

  12. Ex. 5: Solve -2| x + 1 | + 5 > -3 -2| x + 1| + 5 > -3 -5 -5 -2| x + 1| > -8 | x + 1| < 4

  13. Ex. 5 cont. x + 1 > -4 x + 1 < 4 -1 -1 -1 -1 x < 3 x > -5

  14. Solve check understanding 5 p. 35

  15. Ex. 6: The area A in square inches of a square photo is required to satisfy 8.5 < A < 8.9. Write this requirement as an absolute value inequality. Find the tolerance. Find the average of the maximum and minimum values -.2 < A – 8.7 < .2 Write the inequality Rewrite as an absolute value inequality | A – 8.7 | < .2

  16. Homework p. 36 – 37 # 1 – 53 eoo

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