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).