Which inequality symbol represents the phrase "no more than"?

A. ≥ (greater than or equal to)

B. ≤ (less than or equal to)

C. < (less than)

D. > (greater than)

Answer

The inequality symbol that represents the phrase "no more than" is ≤ (less than or equal to). This symbol indicates that a value cannot exceed a specific maximum. For example, a score of no more than 80 can be expressed as a score≤80.

Explanation

The inequality symbol that represents the phrase "no more than" is ≤ (less than or equal to).

In mathematics, the phrase "no more than" indicates a limit or a maximum value that should not be exceeded. The symbol ≤, known as "less than or equal to," captures this meaning perfectly. When we use x≤a, we are saying that the value of x can be anything that is less than or equal to a.

For example:

If you say that a student can have no more than 80 points on a test, we can write this as:

score≤80

This means the student's score can be 80 points, or any value less than that, such as 79, 70, etc. It does not allow for any value greater than 80, which aligns with the phrase "no more than."

If, on the other hand, we were to use the symbol < (less than) alone, it would imply the score could only be any number less than 80, but not 80 itself. Hence, to convey the concept of "no more than," the appropriate symbol is ≤.