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Graphing Linear Inequalities
Notation.
x ≤ y means x is less than or equal to y.
x ≥ y means x is greater than or equal to y.
x < y means x is less than y.
x > y means x is greater than y.
The last two inequalities are called strict inequalities.
Our focus will be on the
nonstrict inequalities .
Algebra of Inequalities
Suppose
x + 3 < 8.
Addition works like for equations:
x + 6 < 11 ( added 3 to each side ).
Subtraction works like for equations :
x + 2 < 7 ( subtracted 4 from each side ).
Multiplication and division by positive numbers work like for equations:
2x + 12 < 22 ⇒ x + 6 < 11
(each side is divided by 2 or multiplied by 1/2).
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