Algebra 1 Common Core Student Edition, Grade 8-9

Think
W h y m u ltip ly b y 3?
You can m u ltip ly by
any m u ltip le o f 3. But
m u ltip ly in g by 3 isolates
the variable.

Here' s W h y It W o r k s M ultiplying or dividing each side of an inequality by

a negative n u m b e r changes th e m ean in g of th e inequality. You n e e d to reverse the

inequality sym bol to m ake th e inequality true. Here is a n example:

3 > 1

-2 (3 ) ■-2 (1 ) Multiply b y -2.

-6 ■—2 Simplify.

-6 < - 2 Reverse the inequality symbol to make the inequality true.

Multiplying by a Positive Number

What are the solutions of | < — 2? Graph the solutions.

• < — 3 2

I 3^|j<3(—2) Multiply each side by 3.

x < —6 Simplify.

1 I 0 —I 1 ----- 1 ----- 1 —►

—9 - 8 - 7 - 6 - 5 - 4 - 3 - 2

£ G o t It? 1. W hat are th e solutions of | > |? G raph th e solutions.

J

) M u l t i p l y i n g b y a N e g a t i v e N u m b e r

q

What are the solutions of — j w S3? Graph and check the solutions.

Think

M u ltip ly in g by a n e g a tive

number changes the

inequality. Reverse the

in e q u a lity sym b ol to make it a

true statement.

Write

-|w > 3

• f ( - f w U - f ( 3 )

<-+■ H h H-----

-6 - 5 - 4 -3 -2-10 1

To check th e e n d p o in t o f

w < - 4 , make sure that - 4

is th e s o lu tio n o f th e e q u a tio n

-lw = 3.

-f( —4 ) ^ 3

3 = 3

To check th e in e q u a lity sym bol

of w s - 4 , make sure th a t

a n u m b e r less th a n - 4 is

a s o lu tio n o f th e o rig in a l

inequality.

3|>3

0

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