**Multiplying
or
Dividing
by a
"positive
number"**
will not
change the
direction
of the
inequality
sign.

Multiplying
inequalities
by a
"positive
number".

**a**
= any real
number,
**b**
= any real
number,

**c**
= a
"positive"
real
number
not equal
to
0

If
**a**
**b**
,
**
then**
**a
*
c**
**b
*
c**

**ac**
**bc**

If
**a**
**b**
,
**
then**
**a
*
c**
**b
*
c**

**ac**
**bc**

If
**a**
**b**
,
**
then**
**a
*
c**
**b
*
c**

**ac**
**bc**

If
**a**
**b**
,
**
then**
**a
*
c**
**b
*
c**

**ac**
**bc**

If
**a**
= 4,
**b**
= 2,
**c**
= 2

If
**4**
**2**
,
**
then**
**4
*
2**
**2
*
2**

**8**
**4**

If
**a**
= 4,
**b**
= 6,
**c**
= 2

If
**4**
**6**
,
**
then**
**4
*
2**
**6
*
2**

**8**
**12**

Dividing
inequalities
by a
"positive
number".

**a**
= any real
number,
**b**
= any real
number,

**c**
= a
"positive"
real
number
not equal
to
0

If
**a**
**b**
,
**
then**
**a
÷
c**
**b
÷
c**

**
**
**
**

If
**a**
**b**
,
**
then**
**a
÷
c**
**b
÷
c**

**
**
**
**

If
**a**
**b**
,
**
then**
**a
÷
c**
**b
÷
c**

**
**
**
**

If
**a**
**b**
,
**
then**
**a
÷
c**
**b
÷
c**

**
**
**
**

If
**a**
= 4,
**b**
= 2,
**c**
= 2

If
**4**
**2**
,
**
then**
**4
÷
2**
**2
÷
2**

**2**
**1**

If
**a**
= 4,
**b**
= 6,
**c**
= 2

If
**4**
**6**
,
**
then**
**4
÷
2**
**6
÷
2**

**2**
**3**

**Multiplying
or
Dividing
by a
"negative
number"**
will
change the
direction
of the
inequality
sign.

Multiplying
inequalities
by a
"negative
number".

**a**
= any real
number,
**b**
= any real
number,

**c**
= a
"positive"
real
number
not equal
to
0

If
**a**
**b**
,
**
then**
**a
*
(-c)**
**b
*
(-c)**

**-ac**
**-bc**

If
**a**
**b**
,
**
then**
**a
*
(-c)**
**b
*
(-c)**

**-ac**
**-bc**

If
**a**
**b**
,
**
then**
**a
*
(-c)**
**b
*
(-c)**

**-ac**
**-bc**

If
**a**
**b**
,
**
then**
**a
*
(-c)**
**b
*
(-c)**

**-ac**
**-bc**

If
**a**
= 4,
**b**
= 2,
**c**
= 2

If
**4**
**2**
,
**
then**
**4
*
(-2)**
**2
*
(-2)**

**-8**
**-4**

If
**a**
= 4,
**b**
= 6,
**c**
= 2

If
**4**
**6**
,
**
then**
**4
*
(-2)**
**6
*
(-2)**

**-8**
**-12**

Dividing
inequalities
by a
"negative
number".

**a**
= any real
number,
**b**
= any real
number,

**c**
= a
"positive"
real
number
not equal
to
0

If
**a**
**b**
,
**
then**
**a
÷
(-c)**
**b
÷
(-c)**

**
**
**
**

**
**
**
**

If
**a**
**b**
,
**
then**
**a
÷
(-c)**
**b
÷
(-c)**

**
**
**
**

**
**
**
**

If
**a**
**b**
,
**
then**
**a
÷
(-c)**
**b
÷
(-c)**

**
**
**
**

**
**
**
**

If
**a**
**b**
,
**
then**
**a
÷
(-c)**
**b
÷
(-c)**

**
**
**
**

**
**
**
**

If
**a**
= 4,
**b**
= 2,
**c**
= 2

If
**4**
**2**
,
**
then**
**4
÷
(-2)**
**2
÷
(-2)**

**-2**
**-1**

If
**a**
= 4,
**b**
= 6,
**c**
= 2

If
**4**
**6**
,
**
then**
**4
÷
(-2)**
**6
÷
(-2)**

**-2**
**-3**

Multiplying
and
Dividing
an
inequality
by 0
(zero).

Multiplying
inequalities
by 0
(zero).

**a**
= any real
number,
**b**
= any real
number

If
**a**
**b**
,
**
then**
**a
*
0**
**b
*
0**

**0**
**0**

If
**a**
= 4,
**b**
= 2

If
**4**
**2**
,
**
then**
**4
*
0**
**2
*
0**

**0**
**0**

*
Dividing
inequalities
by 0
(zero)*-
undefined
(cannot be
done).

**a**
= any real
number,
**b**
= any real
number

If
**a**
**b**
,
**
then**
**a
÷
0**
(undefined)

**b
÷
0**
(undefined)

If
**a**
= 4,
**b**
= 2

If
**4**
**2**
,
**
then**
**4
÷
0**
(undefined)

**2
÷
0**
(undefined)