Addition property of inequalities

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

So…

Since 3 < 5Then 3 + 2 < 5 + 2

Is this true?Yes!

3 + 2 < 5 + 2because 5 < 7

3 + 2 = 5and

5 + 2 = 7

So then…

Since 2 + a < 10Then 2 + a +(-2) < 10 +(-2)

Or 2 + a < 10

Now graph it!

-2 -2a < 8

3 4 5 6 7 8 9 10 11 12

Multiplication Property of Inequalities

If a < b, then a • c < b • calso

If a < b, then < c

a

c

b

So…

Since 3 < 5Then 3 • 2 < 5 • 2

Is this true?Yes!

3 • 2 < 5 • 2because 6 < 10

3 • 2 = 6and

5 • 2 = 10

2

Also…

Since 2a < 10Then 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

1

2

1

2

How about this?

Since 3 < 5Then 3 • -2 < 5 • -2

Is this true?NO!

3 • -2 < 5 • -2because -6 < -10

3 • -2 = -6and

5 • -2 = -10

-2-2

OMG! How about this?

-2a < 10Then -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

2

1

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 < 5Then 3 • -2 5 • -2

But first…Is this true?

YES! but only if you flip the inequality

3 • -2 < 5 • -2

3 • -2 = -6and

5 • -2 = -10

<

Try again

Since 3 < 5Then 3 • -2 5 • -2

But first…Is this true?

YES! but only if you flip the inequality

3 • -2 > 5 • -2because -6 > -10

3 • -2 = -6and

5 • -2 = -10

>

-2-2

Now, try this again.

-2a < 10Then -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 = -4When -2a < 10

Then is -2(-4) < 10

2

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