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Compound Inequalities

Compound Inequalities. Goal: Write, solve and graph compound inequalities. Prepare to have your mind blown!! . What are Compound Inequalities?. Compound Inequalities: two inequalities connected by and or or . Example: x is less than five and greater than -10 or -10 < x < 5.

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Compound Inequalities

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  1. Compound Inequalities Goal: Write, solve and graph compound inequalities. Prepare to have your mind blown!! 

  2. What are Compound Inequalities? • Compound Inequalities: two inequalities connected by andor or. Example: x is less than five and greater than -10 or -10 < x < 5

  3. THE “OR” STORY • LETS NOW SUPPOSE THAT YOU HAD EXHIBITED SUCH GOOD BEHAVIOR THAT YOUR MOM TOLD YOU THAT SHE WOULD GO TO WALMART OR K-MART TO TRY TO FIND YOU A NEW GAME THAT YOU HAVE BEEN WANTING FOR MONTHS. • …SHE LATER TOLD YOU THAT SHE WENT TO K MART AND THEY DIDN’T HAVE IT, SORRY! • DID SHE KEEP HER PROMISE?

  4. THE “AND” STORY • SUPPOSE THAT YOU HAD EXHIBITED SUCH GOOD BEHAVIOR THAT YOUR MOM TOLD YOU THAT SHE WOULD GO TO WALMART AND K-MART TO TRY TO FIND YOU A NEW GAME THAT YOU HAVE BEEN WANTING FOR MONTHS. • …SHE LATER TOLD YOU THAT SHE WENT TO K MART AND THEY DIDN’T HAVE IT, SORRY! • DID SHE KEEP HER PROMISE?

  5. Writing Compound Inequalities From Words • x is greater than 2 and less than or equal to 10 • x is less than -7 or greater than 3

  6. Writing Compound Inequalities (AND) • Let’s Break it Down

  7. Writing Compound Inequalities (OR)

  8. Real Life Compound Inequalities Write and inequality to describe the Alpine meadow region. (use y is represent region)

  9. Real Life Compound Inequalities Write and inequality to describe the Timber Region. (use y is represent region)

  10. Graphing Compound Inequalities • AND  connect together (one line segment) • OR  two separate lines

  11. Let’s Try (AND Ex. 1) -2 < x < 5 • Break it up: x > -2 AND x < 5

  12. Let’s Try (AND Ex. 2) -9 ≤ x < -1

  13. Let’s Try (AND Ex. 3) -5 ≤ x ≤ 4

  14. Let’s Try (OR Ex. 1) x < -6 or x > 4 • Break it up: x < -6 OR x > 4

  15. Let’s Try (OR Ex. 2) x ≤ -1 or x > 3

  16. Let’s Try (OR Ex. 3) x < -8 or x ≥ 8

  17. Questions?! HOMEWORK: Graphing Compound Inequalities Worksheet

  18. Compound Inequalities (cont.)SOLVING

  19. Solving a Compound Inequality with OR • Solve both inequalities separately.

  20. Solving a Compound Inequality with OR 3x + 1 < 4 or 2x – 5 > 7

  21. Solving a Compound Inequality with OR – Ex. 2 • Solve both inequalities separately. 2x + 3 < -1 or 3x – 5 > -2

  22. Solving a Compound Inequality with OR – Ex. 3 2x - 1 < -7 or 7x – 7 > 7

  23. Solving Compound Inequalities with AND • Do all steps to all parts of inequality. -2 ≤ 3x – 8 ≤ 10

  24. Solving Compound Inequalities with AND – Ex. 2 7 < x + 4 < 8

  25. Solving Compound Inequalities with AND – Ex. 3 -15 < 2x - 5 < 9

  26. Multiplying or Dividing by a Negative • When multiplying or dividing a compound inequality by a negative you MUST SWITCH BOTH SIGNS!!!!

  27. Example 1 -2 < -3x – 2 < 1

  28. Example 2 -8 < -6x – 2 < 16

  29. Homework  • Pg. 349 Numbers 12 – 24 evens • SHOW WORK!!

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