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Course 2: Inequalities

Course 2: Inequalities. Objectives: To determine whether a number is a solution of an inequality To graph inequalities on the number line To write inequalities . Inequalities. An inequality is a mathematical sentence containing >, <, > , < . Inequalities. Inequalities.

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Course 2: Inequalities

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  1. Course 2: Inequalities Objectives: To determine whether a number is a solution of an inequality To graph inequalities on the number line To write inequalities

  2. Inequalities • An inequality is a mathematical sentence containing >, <, >, <.

  3. Inequalities

  4. Inequalities • Any number that makes an inequality true is a solution of the inequality. • Inequalities have many solutions. • Example: x > 4 • List 4 possible solutions. 4.5, 5, 7, 12.5

  5. Example 2 The solutions are shown by shading a number line. Example: x > 4 3 4 5 6 7

  6. Example 1 Determine whether each number is a solution of a) 3 yes, because 3 is less than 7 b) -2 yes, because -2 is less than 7 c) 9 no, because 9 is not less than or equal to 7 d) 7 yes, because 7 is equal to 7

  7. 1) Graph m > 3 on a number line. 1 2 3 4 5

  8. 2) Graph k < -2 on a number line. -3 -2 -1 0 1

  9. 3) Graph h > 3 on a number line. 3 4 0 1 2

  10. 4) Graph k < -2 on a number line. -3 -2 -1 0 1

  11. Solving One-Step Inequalities by Adding or Subtracting • 1) x + 4 > 8 - 4 - 4 x > 4

  12. Check x + 4 > 8 • Solution: x > 4 • Substitute a value that is greater than 4 for x. 5 + 4 > 8 9 > 8  This is a true statement.

  13. Graph x > 4 1 2 3 4 5

  14. Solving One-Step Inequalities by Adding or Subtracting • 2) c - 3 < 2 + 3 + 3 c < 5

  15. Check c – 3 < 2 • Solution: c < 5 • Substitute a value that is less than or equal to 5 for c. 5 – 3 < 2 2 < 2  This is a true statement.

  16. Graph c < 5 on a number line. 2 3 4 5 6

  17. Solving One-Step Inequalities by Adding or Subtracting • 3) d - 4 < -2 + 4 + 4 d < 2

  18. Check d – 4 < -2 • Solution: d < 2 • Substitute a value that is less than 2 for d. 1 – 4 < -2 -3 < -2  This is a true statement.

  19. Graph d < -2. -5 -4 -3 -2 -1

  20. Solving One-Step Inequalities by Adding or Subtracting • 4) a - 2 > 6 + 2 + 2 a > 8

  21. Check a - 2 > 6 • Solution: a > 8 • Substitute a value that is greater than or equal to 8 for a. 8 - 2 > 6 6 > 6  This is a true statement.

  22. Graph a > 8. 9 5 6 7 8

  23. Solving One-Step Inequalities by Adding or Subtracting • 5) p - 7 > 0 + 7 + 7 p > 7

  24. Check p - 7 > 0 • Solution: p > 7 • Substitute a value that is greater than 7 for p. 8 - 7 > 0 1 > 0  This is a true statement.

  25. Graph p > 7 4 5 6 7 8

  26. Solving One-Step Inequalities by Adding or Subtracting • 6) j + 5 < 2 - 5 - 5 j < -3

  27. Check j + 5 < 2 • Solution: j < -3 • Substitute a value that is less than or equal to -3 for c. -3 + 5 < 2 2 < 2  This is a true statement.

  28. Graph j < -3 on a number line. -5 -4 -3 -2 -1

  29. Review

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