what does at most in inequality mean
The Correct Answer and Explanation is:
Correct Answer:
In inequality, “at most” means that the value is less than or equal to a certain number. It is written using the symbol ≤.
300-word Explanation:
In mathematics, the phrase “at most” is used to describe a limit or upper boundary that a number cannot exceed. When we say a number is at most a certain value, we are saying that it can be equal to that value or any number smaller than it, but not greater.
For example, if a teacher tells a student, “You can have at most 5 pieces of candy,” it means the student can take 0, 1, 2, 3, 4, or 5 pieces, but not more than 5. This is the same as writing an inequality like:
x ≤ 5
Here, x represents the number of candies. The symbol ≤ means “less than or equal to.” This is what “at most” translates to in math.
This phrase is often used in word problems, especially in topics related to budgeting, capacity, time limits, or measurements. For instance, if a vehicle can carry at most 800 kg, then the load must be 800 kg or less, never more.
It is important not to confuse “at most” with similar terms like “more than,” “less than,” or “at least.” Here is a quick comparison:
- At most: less than or equal to (x ≤ value)
- At least: greater than or equal to (x ≥ value)
- Less than: strictly smaller (x < value)
- More than: strictly larger (x > value)
Understanding “at most” is essential for solving real-world math problems and correctly setting up inequalities. It helps in interpreting limits and boundaries in everyday situations and mathematical contexts.
