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.
||Relation Symbols and their
||Logical (negative) equivalents:
||= is, equals
||≠ not equal (not an equivalent)
||< is less than
is not greater than or equal
||≤ is less than or equal
is not greater than
||> is greater than
is not less than or equal
||≥ 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.
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