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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