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Chapter 3-Inequalities

Chapter 3-Inequalities. Lesson 3.5. Solving Compound Inequalities. Vocabulary. Compound Inequality Two inequalities that are joined by the word and or the word or . Writing a compound inequality . Let’s say you have the inequalities: X ≥ -5 AND X ≤ 7

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Chapter 3-Inequalities

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  1. Chapter 3-Inequalities

  2. Lesson 3.5 Solving Compound Inequalities

  3. Vocabulary • Compound Inequality • Two inequalities that are joined by the word andor the word or

  4. Writing a compound inequality • Let’s say you have the inequalities: • X ≥ -5 AND X ≤ 7 • You can join them together as a COMPOUND INEQUALITY by writing it this way: • -5 ≤ X ≤ 7

  5. Formula for Compound Inequality Smaller Number Larger Number Inequality Sign Inequality Sign Variable

  6. Graphing Compound Inequalities • Use a number line to graph inequalities. • Graph -5 ≤ X ≤ 7 • The black shaded portion represents the compound inequality above -7 -6 -5 -4 -3 -2 –1 0 1 2 3 4 5 6 7 8

  7. Write and Graph the following Compound Inequalities • All real numbers that are AT LEAST -2 and AT MOST 4. x ≤ 4 and x ≥ -2 -2 ≤ x ≤ 4

  8. Write and Graph the Compound Inequality • Temperatures that are ABOVE 32 degrees but NOT AS HIGH AS 40 degrees. t > 32 and t < 40 32 < t < 40

  9. Solving a Compound Inequality Containing AND • Solve -4 < x – 5 ≤ -1 • First step: • Write the compound inequality as TWO inequalities joined by AND -4 < x – 5 AND x – 5 ≤ -1

  10. Solving Compound Inequalities Containing AND • Second Step: • Solve each inequality as you normally would. • -4 < x – 5 AND x – 5 ≤ -1 +5 + 5 +5 +5 1 < x AND x ≤ 4 Solution: 1 < x ≤ 4

  11. Examples: • -6 ≤ 3x < 15 • -3 < 2x – 1 < 7 • 7 < -3x + 1 ≤ 13

  12. Writing Compound Inequalities Containing OR • A solution of a compound inequality joined by the word or is any number that makes EITHER inequality true. • Example: • All real numbers that are less than -3 OR greater than 7. X < -3 or X > 7

  13. Graphing Compound Inequalities Containing OR • Use a number line to graph inequalities. • Graph x < -3 or x > 7 -7 -6 -5 -4 -3 -2 –1 0 1 2 3 4 5 6 7 8

  14. Solving a Compound Inequality Containing OR • Solve 4v + 3 < -5 OR -2v + 7 < 1 • First step: • Write the compound inequality as TWO inequalities joined by OR 4v + 3 < -5OR-2v + 7 < 1

  15. Solving Compound Inequalities Containing OR • Second Step: • Solve each inequality as you normally would. • 4v + 3 < –5 OR -2v + 7 < 1 - 3 -3 - 7 -7 4v < -8 -2v < -6 ÷ 4 ÷ 4÷ -2 ÷ -2 v < - 2 OR v > 3 - 2 3

  16. How do I know which symbol to use in a word problem? • Look for these WORD CLUES to help you determine which inequality symbol to use.

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