What inequality sign is no more than
The Correct Answer and Explanation is :
The inequality sign for “no more than” is ≤, which means “less than or equal to.” This symbol is used to express that a value can be equal to or smaller than a given number.
Explanation:
In mathematics, inequality symbols are used to compare two expressions. The most common symbols are:
- <: Less than
- >: Greater than
- ≤: Less than or equal to
- ≥: Greater than or equal to
- =: Equal to
- ≠: Not equal to
When we say “no more than,” we are describing a situation where the value of one quantity cannot exceed another quantity. This implies that the value could either be less than or exactly equal to the other quantity.
For example, consider the statement:
- “You can have no more than 5 apples.”
This means you can have 5 apples, or you could have fewer than 5 apples, but not more than 5. In mathematical terms, this can be written as:
[ x \leq 5 ]
where ( x ) represents the number of apples. The inequality ( x \leq 5 ) includes all values less than 5 and exactly 5, but excludes any value greater than 5.
Why ≤ is used:
The “no more than” phrase reflects a condition where the upper limit is reached, but not exceeded. Therefore, the inequality must allow for the possibility of equality as well as smaller values, which is why “less than or equal to” (≤) is the correct symbol.
In contrast, phrases like “no less than” would correspond to the inequality symbol “≥,” indicating values that are greater than or equal to the specified number.
In summary, “no more than” translates to “less than or equal to,” or ( \leq ), because it allows for values that do not exceed the specified quantity while still including that quantity.