Final answer:
A compound inequality representing 'a quantity x is either less than 9 or greater than 16' is written as 'x < 9 or x > 16'. This inequality allows for two different sets of values for x, those that are less than 9 and those that are greater than 16.
Step-by-step explanation:
To write a compound inequality that represents the sentence 'a quantity x is either less than 9 or greater than 16', we use two inequalities combined with the word 'or' because the statement allows for two different sets of values for x. Specifically, the compound inequality is x < 9 or x > 16.
An inequality symbol is used to show how two values are related. For example, if we say 1.5 ≤ x ≤ 4.5, it means x can be any number between and including 1.5 and 4.5. The compound inequality we're looking for involves a similar concept but with two distinct ranges for the possible values of x.