Linear Inequalities

Linear inequalities are a set of numbers that will meet a certain criteria on the number line

Example: A < x < B

Where x is a number or group of numbers or “sets” that fall between A and B

The notation{x│ } is read “the set of all x such that….” And is called set-builder notation. The vertical bar(│) is read “such that”. A statement following the bar gives a condition or restriction for the variable x

When using interval notation, it is important to note that a parenthesis ( ) indicates non inclusivity and a bracket [ ] indicates inclusivity

So A < x ≤ B could be written

(A , B]

Inequality Symbols

Union and Intersection Notation

Connecting compound inequalities with “and” and “or”

“And” indicates Intersection (∩)

Looking at all numbers that make both statements true

“Or” indicates Union (U)

Looking at numbers that make either inequality true