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Chapter 0: Problem 13

Express each interval in set-builder notation and graph the interval on a number line. $$(-\infty, 5.5)$$

Short Answer

Expert verified
The set-builder notation for the given interval is \{x | x < 5.5\}. On a number line, this interval is represented as all real numbers to the left of 5.5.

Step by step solution

01

Understanding the Interval

The given interval is \(-\infty, 5.5\), which would include all real numbers less than 5.5. It's an open interval, as it doesn't include the number 5.5 itself, which is indicated by the parentheses instead of square brackets.
02

Converting to Set-Builder Notation

The set-builder notation provides a way to describe this kind of intervals. This interval is expressed as \{x | x < 5.5\}, which means the set of all numbers 'x' such that 'x' is less than 5.5.
03

Graphing on a Number Line

To graph this interval on a number line, a line is drawn and a small circle is marked at 5.5 (since 5.5 is not included in the range). An arrow pointing to the left side from 5.5 is then drawn to indicate every real number less than 5.5.

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