Module 9: Background You’ll Need 1

Lumen Learning

Module 9: Background You’ll Need 1

Represent intervals on a number line and using plus/minus notation.

Intervals

Interval notation is a way of describing sets that include all real numbers between a lower bound and an upper bound. These bounds may or may not be included in the set. The endpoint values are listed between brackets or parentheses. A square bracket indicates inclusion in the set, and a parenthesis indicates exclusion from the set.

Inequality	Words	Interval Notation
[latex]{a}\lt{x}\lt{ b}[/latex]	All real numbers between a and b	[latex]\left(a,b\right)[/latex]

Suppose you want to buy a pair of jeans. At department stores, the average cost of jeans may be $30. Suppose at some stores the cost may be up to $5 over that cost, while at other stores the cost may be up to $5 lower than that cost. We can write this using [latex]\pm[/latex] notation as $30 [latex]\pm[/latex] $5. If we subtract 5 from 30, we get $25 [latex](30 – 5 = 25)[/latex], and if we add 5 to 30, we get $35 [latex](30 + 5 = 35)[/latex].

This makes our cost range for department store jeans $25 to $35. In interval notation, this can be represented as [latex]($25, $35)[/latex].

$25 is the lower bound of the cost interval, and $35 is the upper bound of the cost interval.
This can also be represented on a number line by putting a dot in the center at 30 and drawing a line that extends 5 in both directions.