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Addition property of inequalities

Learn how the addition and multiplication properties of inequalities work with examples and rules explained. Understand when to switch inequality signs and graph inequalities. Practice solving equations to master the concepts.

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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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