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1.5 Presentation Transcript

  • 1. 1.5 SOLVING INEQUALITIES
  • 2. INEQUALITIES An inequality is a relationship in which two quantities may not be equal.  Phrases such as “at most” and “at least” suggest this type of relationship
  • 3. WRITING & GRAPHINGINEQUALITIES
  • 4. WRITE THE INEQUALITYTHAT REPRESENTS THESENTENCE. 5 fewer than a number is at least 12 The product of a number and 8 is greater than 25 The quotient of a number and 3 is no more than 15
  • 5. SOLVING INEQUALITIES The solutions of an inequality are the numbers (values) that make it true. We solve inequalities the same way we solve equations  Except:when we multiply or divide by a negative number, we reverse the inequality symbol  Hint: when you solve, put the variable on the LEFT, this ensures that the arrow on the graph points the same way as the pointed end of the inequality symbol
  • 6. SOLVE EACH INEQUALITY.GRAPH THE SOLUTION.2x > 8
  • 7. SOLVE EACH INEQUALITY.GRAPH THE SOLUTION.12 − 2 y ≥ 38
  • 8. SOLVE EACH INEQUALITY.GRAPH THE SOLUTION.5 ( x + 3) ≤ 55
  • 9. SOLVE EACH INEQUALITY.GRAPH THE SOLUTION.−2 ( w + 4 ) + 9 < −13
  • 10. NO SOLUTION OR ALL REALNUMBERS AS SOLUTIONS When solving inequalities, we can reach solutions that seem strange and require analysis.  If we reach a false statement, there are no solutions, and the statement is never true  If the variable(s) drop out and we have a true statement or we reach a point where one side is identical to the other, the statement is always true for all real numbers.
  • 11. IS THE INEQUALITY ALWAYS,SOMETIMES, OR NEVERTRUE?3 ( x + 5 ) < 30
  • 12. IS THE INEQUALITY ALWAYS,SOMETIMES, OR NEVERTRUE?−2 ( 3 x + 1) > −6 x + 7
  • 13. IS THE INEQUALITY ALWAYS,SOMETIMES, OR NEVERTRUE?5 ( 2 x − 3) − 7 x ≤ 3 x + 8
  • 14. COMPOUND INEQUALITIES A compound inequality is an inequality statement that joins two inequalities using the word and or the word or.
  • 15. COMPOUND INEQUALITIES To solve a compound inequality containing and:  Find all values of the variable that make both inequalities true
  • 16. SOLVE THE COMPOUNDINEQUALITY. GRAPH THESOLUTION.7 < 2 x + 1 and 3 x ≤ 18
  • 17. SOLVE THE COMPOUNDINEQUALITY. GRAPH THESOLUTION.3 < 2 x + 1 < 11 This is a collapsed “and inequality”
  • 18. COMPOUND INEQUALITIES To solve a compound inequality containing or:  Find all values of the variable that make at least one of the inequalities true.
  • 19. SOLVE THE COMPOUNDINEQUALITY. GRAPH THESOLUTION.7 + k ≥ 6 or 8 + k < 3
  • 20. SOLVE THE COMPOUNDINEQUALITY. GRAPH THESOLUTION.7 w + 3 > 11 or 4 w − 1 < −13
  • 21. HOMEWORK Page 38  #11– 23, 29 – 43, 45 – 49, 59 – 61 odds only