Which of the following describe the sum p+(-q) where p and q are positive numbers?

Question

A. the sum p + (-q) is the number located a distance from |q| in a positive direction
B. the sum p+ (-q) is the number located a distance from |q| in a negative direction
C. the sum p+ (-q) is the number located a distance from |p| in a negative direction
D. the sum p+ (-q) is the number located a distance from |p| in a positive direction

Answer 1

To analyze the expression \( p + (-q) \), we can rewrite it as \( p - q \).

Since \( p \) and \( q \) are both positive numbers, the result \( p - q \) will depend on the relative sizes of \( p \) and \( q \):

1. If \( p > q \), then \( p - q \) will be positive.
2. If \( p < q \), then \( p - q \) will be negative.
3. If \( p = q \), then \( p - q \) will equal zero.

Now let's examine the given options:

A. The sum \( p + (-q) \) is the number located a distance from \( |q| \) in a positive direction.

• This can be interpreted as “starting from \( |q| \) and moving to the right.” However, whether the result is in the positive direction depends on the values of \( p \) and \( q \). So this is not necessarily true.

B. The sum \( p + (-q) \) is the number located a distance from \( |q| \) in a negative direction.

• This statement similarly depends on \( p \) and \( q \) and cannot be generally stated as true.

C. The sum \( p + (-q) \) is the number located a distance from \( |p| \) in a negative direction.

• This would imply moving left from \( |p| \), which again is not always valid, as the interpretation depends on the relationship between \( p \) and \( q \).

D. The sum \( p + (-q) \) is the number located a distance from \( |p| \) in a positive direction.

• This statement suggests moving right from \( |p| \), which is also conditional, depending on \( p \) and \( q \).

In conclusion, none of the options A, B, C, or D accurately capture the nature of \( p + (-q) \) universally. The output can vary significantly based on the specific values of \( p \) and \( q \).

If you are looking for a safer analysis, you could say that the result of \( p - q \) means we are determining a value based on the difference between two positive numbers, resulting in something that could be positive, negative, or zero depending on their relative sizes, thus none of the statements apply universally.

Answer 2

try again

Answer 3

Let's analyze the expression \( p + (-q) \), which simplifies to \( p - q \). Given that \( p \) and \( q \) are positive numbers, let's clarify its behavior and relate it to the options provided:

1. If \( p > q \):

   • The result \( p - q \) will be positive.

2. If \( p < q \):

   • The result \( p - q \) will be negative.

3. If \( p = q \):

   • The result \( p - q \) will equal zero.

Now, let's examine the options carefully:

A. The sum \( p + (-q) \) is the number located a distance from \( |q| \) in a positive direction.

• This suggests that we're considering the value as being \( |q| + k \) for some distance \( k > 0\). This could only be true when \( p > q \), as the result is then positive. Overall, this statement cannot be universally correct.

B. The sum \( p + (-q) \) is the number located a distance from \( |q| \) in a negative direction.

• This would mean subtracting, or moving left from \( |q| \). This statement suggests that the result is valid when \( p < q \). So, like option A, it's also conditional and not true in all cases.

C. The sum \( p + (-q) \) is the number located a distance from \( |p| \) in a negative direction.

• This suggests moving left from \( |p| \). This would be incorrect because moving negatively from \( |p| \) does not accurately describe \( p - q \); it varies depending on whether \( p \) is greater or smaller than \( q \).

D. The sum \( p + (-q) \) is the number located a distance from \( |p| \) in a positive direction.

• This implies a movement right (or adding) from \( |p| \), which doesn't accurately depict the scenario where \( q \) plays a crucial role in determining if \( p - q \) is positive or negative.

Let's focus back on what \( p - q \) means:

• If \( p > q \), the result will be a positive number.
• If \( p < q \), the result will be a negative number.
• If \( p = q \), the result is zero.

Considering all the explanations and conditions, the best way to describe \( p + (-q) \) focusing on the distance from either positive or negative reference, based on the relation between \( p \) and \( q \), would best fit with:

A when \( p > q \) or B when ( p < q**.

Since the question asks for statements that can describe \( p + (-q) \), if we’re required to pick one definition that can encompass more scenarios, we can infer:

• The sum describes a situation dependent on the relative values of \( p \) and \( q\), but if we had to select one, neither perfectly describes the entire range without failing under certain conditions.

If the selections must be limited to just one, B can be argued as closest, since \( p - q \) in terms of distance from \( |q| \) for values \( p < q \) would lead to a negative outcome.

However, it’s critical to state that these options mainly serve contrasting conditions rather than being universally correct for all positive values of \( p \) and \( q \). If you want any specific focus within the conditions of \( p \) and \( q\), please clarify, and I can assist further!