Inequalities in one Variable
In this section we will learn how to use the relation symbols in word sentences and
how to translate them into mathematical sentences.
Comparison Symbols
English terms; 
Relation Symbols and their 
Logical (negative) equivalents:

English 
Relation 
Negation (opposite)

equals 
= is, equals 
≠ not equal (not an equivalent) 
less than 
< is less than 
is not greater than or equal

at most 
≤ is less than or equal 
is not greater than 
beyond 
> is greater than 
is not less than or equal 
at least 
≥ is greater than or equal 
is not less than 
Rules of Order of Operations
Please Pardon My Dear Aunt Sally
Parentheses (Grouping): Work from inside out.
Powers (Exponents): Simplify all powers first.
Multiply and/or
Divide: Work left to right (watch signs).
Add and/or Subtract: Combine like terms only.
Properties of Inequalities
For any real numbers a, b, and c:
1. EQUIVALENT PROPERTY:
a < b ↔ b > a
2. ADDITION PROPERTY:
If a < b is true then a + c < b + c is true.
3. MULTIPLICATION PROPERTY:
For c > 0, if a < b is true then a Â·c < b Â·c is true.
For c < 0, if a < b is true then a Â·c > b Â·c is true.
NOTE: Negation reverses every sign in its path. (1)Â·(2 < 3)
↔ +2 > 3
