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3 4b compound inequalities

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  • 1. 3-4 Extension Compound Inequalities

2. Compound Inequalities Formed by joining two inequalities with the word and or or. Examples: and or 3. Example 1: Write as a single inequality and then graph: x > -8 and x 4 4. Example 2: Graph y 0 or y 7 5. You Try! Graph each compound inequality: k > 3 and k < 9 w < -10 or w -6 6. Writing From Graphs Write a compound inequality for: 7. Example Write a compound inequality for: 8. You Try! Write an inequality for: 9. Solving with and Solve like an equation, but do each thing to all 3 parts! Example: 4 < x 5 < 7 10. Example Solve and graph the solution. -3 < -2x + 1 9 11. You Try! Solve and graph the solution. -1 2x + 3 < 7 12. Solving with or Solve each inequality separately. Be sure to keep the or in your answer! Example: b + 7 < 2 or 2b < 8 13. Example Solve and graph the solution. 3x- 5 < -8 or 2x 1 > 5 14. You Try! Solve and graph the solution. 4x + 1 -11 or 3x 4 5 15. Absolute Value Inequalities Remember absolute value can be used for distance. Example: |x| < 2 Means the distance between x and 0 is less than 2 Can be written -2 < x < 2 16. |x| > 2 Means the distance between x and 0 is greater than 2 Can be written x < -2 or x > 2 17. Solving Abs. Value For less than rewrite as and |ax + b| < c -c < ax + b < c For greater than rewrite as or |ax + b| > c ax + b < -c or ax + b > c 18. Example Solve and graph: |x + 7| 2 19. Example Solve and graph: |x 3| 4 20. You Try! Solve and graph: |4x 5| 11 |2x + 5| 8 21. No Solution Can an absolute value expression ever be negative? NO!! So, inequalities like: |x| < -1 |x| -2 have no solution. 22. All Real Numbers When is an absolute value expression positive? ALWAYS! So, inequalities like: |x| > -1 |x| -2 have solution all real numbers. 23. You Try! Tell if each inequality has no solution or all real numbers. |x| > -6 |x 7| < -1 |3x + 9| -4 |x + 6| < 0

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