Final answer:
In mathematics, when fewer than a certain number is mentioned without the possibility of it being exactly the number, use the '<' symbol for less than. If the exact number is included, use the '≤' symbol for less than or equal to. Understanding which inequality symbol to use is a key concept in Mathematical comparisons.
Step-by-step explanation:
To choose the correct inequality symbol, we need to identify the context of the situation. If we are talking about a scenario where we have fewer than a certain number of items, we use the '<' symbol to represent 'less than'. This indicates that the number of items we have is less than the specified number. For example, if you have fewer than 10 apples, this would be written as 'number of apples < 10'.
However, if the sentence indicates that we can have exactly the number of items as well as fewer, we need to use the '≤' symbol, which represents 'less than or equal to'. For instance, if 70% of students answered 16 or fewer questions correctly, we would say their score ≤ 16. In cases where the exact value is included as a possibility along with lower values, the '≤' is the appropriate choice.
Understanding inequalities in Mathematics involves comparing numbers or quantities using symbols such as '<' (less than), '>' (greater than), '≤' (less than or equal to), and '≥' (greater than or equal to).