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 ·c < b ·c is true.
For c < 0, if a < b is true then a ·c > b ·c is true.
NOTE: Negation reverses every sign in its path. (-1)·(-2 < 3)
↔ +2 > -3
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