# Which is Simpler: |k|=5 or k=±5?

• bomba923
In summary, the main difference between |k|=5 and k=±5 is the type of notation used. |k|=5 represents the absolute value of k, while k=±5 means that k can be positive or negative 5. Both notations are equivalent in terms of mathematical meaning, but may be preferred in different situations. For example, if the focus is on finding the distance from 0, |k|=5 may be more appropriate, while if the solutions for k are needed, k=±5 may be more useful.
bomba923
Which is "simpler"?---i.e., considered more "simplfied" ?

$$\left| k \right| = 5$$ OR $$k = \pm 5$$ ?

It's really about relevance. For example if it is a matter of drawing a graph like $f(k) = k^2 - 25$ and you want to express the fact at the point f(k) = 0 there are two solutions you would probably write $k = \pm 5$.

However, if it is something physical like and related to magnitude you might want to express it as $|k| = 5$

Both expressions are equally simple and simplified. They both represent the same concept, which is the absolute value of k being equal to 5. The only difference is the notation used. The first expression uses the absolute value notation, while the second expression uses the plus-minus notation. Both notations are commonly used and understood, so it ultimately comes down to personal preference or the context in which the expression is being used. In terms of simplicity, they are both considered to be equally simplified and straightforward.

## 1. What is the difference between |k|=5 and k=±5?

The main difference between |k|=5 and k=±5 is the type of notation used. |k|=5 represents the absolute value of k, meaning the distance of k from 0 on the number line is 5. On the other hand, k=±5 means that k can be either positive or negative 5, giving two possible solutions for k.

## 2. Which notation is simpler to understand?

This can vary depending on the individual, but in general, |k|=5 may be seen as simpler because it directly states the value of k without any additional symbols or variables.

## 3. Are both notations equivalent?

Yes, both notations are equivalent in terms of mathematical meaning. They both represent the same concept of the value of k being either positive or negative 5.

## 4. In what situations would one notation be preferred over the other?

The choice of notation may depend on the context and the purpose of the problem. If the focus is on finding the distance from 0, then |k|=5 may be preferred. However, if the solutions for k are needed, then k=±5 may be more useful.

## 5. Can you give an example of a problem where one notation is more appropriate than the other?

Consider a problem where the height of a building is represented by k. If we know that the building is 5 stories tall, then |k|=5 would be more appropriate because the focus is on the distance from 0. On the other hand, if we are given the solutions for k, such as k=±5, then k=±5 may be more useful in determining the height of the building.

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