Inequalities
Terms
Acute Angle
-
An angle with a measure of less than 90 degrees.
Addition Properties of Inequality
-
If
a < b
, then
a + c < b + c
If a > b , then a + c > b + c
If a > b , then a + c > b + c
Greater Than
-
a > b
if and only if there is a positive number
c
such that
a - c = b
.
Inequality
-
A statement that shows the relationship between two (or more)
expressions with one of the following five signs:
<
,
≤
,
>
,
≥
,
≠
.
Inequality Properties of Opposites
-
If
a > 0
, then
- a < 0
If a < 0 , then - a > 0
If a < 0 , then - a > 0
Less Than
-
a < b
if and only if there is a positive number
c
such that
a + c = b
.
Multiplication and Division Properties of Inequality
-
For positive numbers:
If a < b and c > 0 , then ac < bc and
< 
If a > b and c > 0 , then ac > bc and >
For negative numbers:
If a < b and c < 0 , then ac > bc and >
If a > b and c < 0 , then ac < bc and <
If a < b and c > 0 , then ac < bc and
<
If a > b and c > 0 , then ac > bc and
>
For negative numbers:
If a < b and c < 0 , then ac > bc and
>
If a > b and c < 0 , then ac < bc and
<
Obtuse Angle
-
An angle with a measure greater than 90 degrees, but not more than 180 degrees.
Property of Squares of Real Numbers
-
a
2≥ 0
for all real numbers
a
.
Right Angle
-
An angle with a measure of exactly 90 degrees.
Subtraction Properties of Inequality
-
If
a < b
, then
a - c < b - c
If a > b , then a - c > b - c
If a > b , then a - c > b - c
Transitive Properties of Inequality
-
If
a < b
and
b < c
, then
a < c
.
If a > b and b > c , then a > c .
If a > b and b > c , then a > c .
Trichotomy Property
-
For any two real numbers
a
and
b
, exactly one of the following is
true:
a < b
,
a = b
,
a > b
.
