# Addition property of inequalities If a < b, then a + c < b + c.

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

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

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

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

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

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

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

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

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

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

Try again 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 3 -2 = -6 and 5 -2 = -10 <

Try again 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 3 -2 = -6 and 5 -2 = -10 >

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

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