Intervals and Inequalities World 3-3 Intervals and Inequalities

Eg 1. Place the following #’s on a number line. -6, 5 , 251/2, -1 & - 10 2 3 -1 3 5 2 -6 - 10 251/2 2 4 6 8 10 -2 -4 -6 -8

Sometimes it is useful to talk about a RANGE of numbers. There are 3 ways to accomplish this.

Identifies the interval of numbers The end number IS in the set 1) Number Line 2 4 6 8 10 -2 -4 -6 -8 Identifies the interval of numbers The end number IS in the set The end number IS NOT in the set

2) Bracket Notation [ -2, 8 [ Lowest # Highest # -5, 7 [ ] 5, 9 ] [ HUGGING brackets mean the end number it is CONTAINED in the set. BACK FACING brackets means the end number is NOT CONTAINED in the set.

Greater than 10 _________ At Most 22 _________ At Least 15 _________ Eg. 2 Inequalities Language The mouth always OPENS to the larger number. x 5 x 10 Less than 5 _________ Greater than 10 _________ At Most 22 _________ At Least 15 _________ x 22 x 15

3) Set Notation { x R | -2 x 8 } x is a real # Lowest # Highest #

Intervals [a,b] [a,b[ ]a,b] ]a,b[ Closed Left Closed Right Open Bracket Set-Builder Number Line Closed Left Closed Right Open Left Open Right Closed Open [a,b] b a b a [a,b[ ]a,b] b a b a ]a,b[

World 3-3