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Addition property of inequalities

Addition property of inequalities. If a < b, then a + c < b + c. So…. 3 + 2 = 5 and 5 + 2 = 7. Since 3 < 5 Then 3 + 2 < 5 + 2 Is this true? Yes! 3 + 2 < 5 + 2 b ecause 5 < 7. So then…. Since 2 + a < 10 Then 2 + a +(-2) < 10 +(-2) Or 2 + a < 10 Now graph it!. -2. -2. a < 8.

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Addition property of inequalities

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  1. Addition property of inequalities

  2. If a < b, then a + c < b + c

  3. So… 3 + 2 = 5 and 5 + 2 = 7 Since 3 < 5 Then 3 + 2 < 5 + 2 Is this true? Yes! 3 + 2 < 5 + 2 because 5 < 7

  4. So then… • Since 2 + a < 10 • Then 2 + a +(-2)< 10 +(-2) • Or 2 + a < 10 • Now graph it! -2 -2 • a < 8 3 4 5 6 7 8 9 10 11 12

  5. Multiplication Property of Inequalities If a < b, then a • c < b • c also If a < b, then <

  6. So… 3 • 2 = 6 and 5 • 2 = 10 Since 3 < 5 Then 3 • 2 < 5 • 2 Is this true? Yes! 3 • 2 < 5 • 2 because 6 < 10

  7. Also… 2 2 Let me pick something less than 5 How about if a = 2 when 2a < 10 Then is 2(2) < 10 Since 2a < 10 Then 2a • < 10 • Or 2a < 10 a < 5 Is this true? Yes! because 4 < 10

  8. How about this? 3 • -2 = -6 and 5 • -2 = -10 Since 3 < 5 Then 3 • -2 < 5 • -2 Is this true? NO! 3 • -2 < 5 • -2 because -6 < -10

  9. OMG! How about this? -2 -2 Let me pick something less than -5 How about if a = -6 when -2a < 10 Then is -2(-6) < 10 -2a < 10 Then -2a • (- ) < 10 • (- ) Or -2a < 10 a < -5 Is this true? NO! What the…? 12 < 10

  10. Oh…I forgot to tell you the special rule. < If a < b, then a • -c b • -c

  11. Oh…I forgot to tell you the special rule. > If you are going to multiply (or divide) each side of an inequality with a negative number, YOU HAVE TO SWITCH THE INEQUALITY SIGN TO MAKE IT TRUE!!!! If a < b, then a • -c b • -c

  12. Try again < 3 • -2 = -6 and 5 • -2 = -10 Since 3 < 5 Then 3 • -2 5 • -2 But first… Is this true? YES!  but only if you flip the inequality 3 • -2 < 5 • -2

  13. Try again > 3 • -2 = -6 and 5 • -2 = -10 Since 3 < 5 Then 3 • -2 5 • -2 But first… Is this true? YES!  but only if you flip the inequality 3 • -2 > 5 • -2 because -6 > -10

  14. Now, try this again. < < -2 -2 Let me pick something morethan -5 How about if a = -4 When -2a < 10 Then is -2(-4) < 10 -2a < 10 Then -2a • (- ) 10 • (- ) Or -2a 10 a > -5 Is this true? YES!!!! Because 8 < 10

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