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Level 208

Properties of Inequality


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No. C must be >0
If A > B, is A/C > B/C?
If A > B and C > D, is A + B > C + D?
Not necessarily. The addition property of inequality only works when you say the two bigger ones are greater than the two little ones.
State the 2 Addition properties of inequality
If a > b, then a + c > b + c; ALSO IF a > b and c > d, then a + c > b + d
State the Multiplication property of Inequality
If a > b and c > 0 then ac > bc
State the Division Property of Inequality
If a > b and c > 0, a/c > b/c
State the Transitive Property of Inequality
If a > b and b > c, then a > c
State the Substitution Property of Inequality
If a = b, then a can be substituted for b in any inequality
State the Three Possibilities Property of Inequality
either a > b, a = b, or a < b
State the Whole Greater than Part Property
If c = a + b and b > 0, then c > a
False. A can equal B. That's the 3 Possibilities Property
True or false? If a ≯ b, then a < b?
Transitive
If x < y and y < 0, what property says x < 0?
Yes, by the addition property
If a > b and c > d, is a + c > b + d?
Whole is Greater than Parts.
If x = y + z and z > 0, what property tells us x > y?
Substitution
The replacement of letters/variables in an algebraic expression.
Three possibilities(Trichotomy)
What property says either x > y, x = y or x < y?
Addition
to join two or more quantities
Multiplication
process of repeated addition
If a=b+c, then a>b
False. True only if c>0
If X-Y-Z , then XY+YZ=XZ, we may conclude XZ>XY ∧XZ>YZ
True. We do not need to worry about any stipulation that one of the distances >0 since distance is defined to be a positive number. The same is true for the sums of the measures of angles.
X+7>3+Y
What may we conclude if X>3 and 7>Y?
a>b or a<b
What may we conclude if a≠b?
Nothing.
x>y and y<7 What may we conclude?
True
Substitution and transitive properties are not interchangeable when dealing with inequalities
7=10+(-3)
If a=b+c, give a numerical example showing that a not greater than b.
addition (property of inequality)
If a < b, then a + c < b + c
subtraction (property of inequality)
If a < b, then a - c < b - c
multiplication (property of inequality)
If a < b and c is positive, then a · c < b · c
division (property of inequality)
If a < b and c is positive, then a ÷ c < b ÷ c
addition (property of equality)
if a = b then a + c = b + c
subtraction (property of equality)
if a = b then a - c = b - c
multiplication (property of equality)
if a = b then a · c = b · c
division (property of equality)
if a = b then a / c = b / c
substitution (property of equality)
if a = b then b can replace a
distributive (property of equality)
a(b+c) = ab + ac
The Law of Trichotomy
Exactly one of the following is true:
Transitive property of Inequality
Given x, y, and z are real numbers
a<b
Less Than
a>b
Greater Than
a≤b
Less Than or Equal To
a≥b
Greater Than or Equal To
The "less than or equal to" sign
The "greater than or equal to" sign
≠ means
not equal
a < b
a is less than b
a > b
a is greater than b
10 >5 is written/read as
10 is greater than 5
5<10 is written/read as
5 is less than 10
A=B
Equality: both sets have the same members
12>5 is read/written as
12 is greater than 5
47 _______ 31
> ; 47>31 .. 47 is greater than 31
38__20
> ; 38>20 .. 38 is greater than 20
91__27
> ; 91>27 .. 91 is greater than 27
22 _______ 11
> ; 22>11 .. 22 is greater than 11
5__9
< ; 5<9 .. 5 is lesser than 9
1_______4
< ; 1<4 .. 1 is lesser than 4
204 _______ 204
= ; 204 is equal to 204
333_______333
= ; 333 is equal to 333
|-2|________|-2.7|
<; |-2|<|-2.7| ... |-2| is lesser than |-2.7|
|-12|__|0|
> ; |-12|>|0| |-12| is greater than |0|
|-5.01| _______ |-5|
>; |-5.01|>|-5| |-5.01| is greater than |-5|
addition property
If a>b, then a+c>b+c
subtraction property
If a>b, then a-c>b-c
multiplication property
If a>b and c>0, then ac>bc
division property
If a>b and c>0, then a/c>b/c
Transitive Property
If a>b and b>c, then a>c