To determine whether the statement is true, we need to analyze [tex]$32 + (-17)$[/tex] and the distance from 32 to the result.
1. Calculate the result of the addition:
[tex]\[
32 + (-17) = 15
\][/tex]
So, the result is 15.
2. Determine the distance from 32 to the result:
The distance between two numbers on a number line is the absolute difference between them.
[tex]\[
|32 - 15| = 17
\][/tex]
Therefore, the distance from 32 to 15 is 17 units.
Now, let's address each part of the statement:
- "32 + (-17) is 17 units from 32"
As we've calculated above, the result of [tex]$32 + (-17)$[/tex] is 15, and the distance (absolute difference) from 32 to 15 is indeed 17 units. So this part of the statement is true.
- "in the positive direction"
When we look at the direction, starting from 32 and moving towards 15, we're actually moving towards the lesser numerical value (which is negative direction in terms of value decreasing direction).
However, typically when referring to the distance, the phrase "in the positive direction" may imply moving forward or simply considering the positive distance value without concern for actual direction. Thus, if interpreted this way to mean no negative signs are considered in the distance, we could still regard this part more symbolically correct.
Summarizing the analysis:
- The distance aspect is correct.
- Positivity could be misinterpreted if assumed direction-based.
So, the provided statement is essentially accurate regarding numerical distance, but slight caution if strictly interpreted direction-wise.
