Answer :
To solve the problem of determining which pair of numbers are not opposites, we need to understand what "opposite numbers" are. Opposite numbers are pairs of numbers that are equal in magnitude but have different signs; essentially, the opposite of a number [tex]\( x \)[/tex] is [tex]\( -x \)[/tex].
Let's examine each pair of numbers given:
1. 17 and [tex]\(|-17|\)[/tex]:
- The number 17 is positive.
- The expression [tex]\(|-17|\)[/tex] represents the absolute value of -17, which is 17.
- So, the pair (17 and 17) are not opposites because they are the same number.
2. 71 and -71:
- Here, one number is positive (71) and the other is negative (-71).
- Since 71 and -71 have the same magnitude but opposite signs, they are opposites.
3. 17 and -17:
- Similarly, the positive 17 and negative 17 have the same magnitude but opposite signs.
- Therefore, these numbers are opposites.
4. [tex]\(|7|\)[/tex] and -7:
- The expression [tex]\(|7|\)[/tex] gives us the absolute value of 7, which is 7.
- We have 7 and -7, which again are numbers with the same magnitude but opposite signs.
- Hence, they are opposites.
After analyzing all the pairs, the pair "17 and [tex]\(|-17|\)[/tex]" are not opposites, because both numbers are actually 17.
Let's examine each pair of numbers given:
1. 17 and [tex]\(|-17|\)[/tex]:
- The number 17 is positive.
- The expression [tex]\(|-17|\)[/tex] represents the absolute value of -17, which is 17.
- So, the pair (17 and 17) are not opposites because they are the same number.
2. 71 and -71:
- Here, one number is positive (71) and the other is negative (-71).
- Since 71 and -71 have the same magnitude but opposite signs, they are opposites.
3. 17 and -17:
- Similarly, the positive 17 and negative 17 have the same magnitude but opposite signs.
- Therefore, these numbers are opposites.
4. [tex]\(|7|\)[/tex] and -7:
- The expression [tex]\(|7|\)[/tex] gives us the absolute value of 7, which is 7.
- We have 7 and -7, which again are numbers with the same magnitude but opposite signs.
- Hence, they are opposites.
After analyzing all the pairs, the pair "17 and [tex]\(|-17|\)[/tex]" are not opposites, because both numbers are actually 17.
