To determine the accuracy of Jillian's translation of the expression [tex]\(9 + n\)[/tex] into words, let's analyze each of the given options one by one.
1. Option 1: "It is incorrect. The variable would come first in the expression 'a number' ( [tex]\(n\)[/tex] ) 'increased by' ( + ) 'nine' (9)."
- This option incorrectly suggests that the order of the numbers matters in addition. However, addition is commutative, which means [tex]\( n + 9 \)[/tex] is the same as [tex]\( 9 + n \)[/tex]. Thus, whether it is written as [tex]\( n + 9 \)[/tex] or [tex]\( 9 + n \)[/tex], the meaning is the same. So, this option is incorrect.
2. Option 2: "It is incorrect. The phrase 'increased by' refers to the inequality symbol 'greater than' ( [tex]\(>\)[/tex] ), not addition."
- This option is incorrect because the phrase "increased by" actually refers to addition, not an inequality. "Increased by" means to add, not to make greater than. So, this option is also incorrect.
3. Option 3: "It is correct. A number increased by nine ([tex]\(n + 9\)[/tex]) is the same as nine increased by a number ([tex]\(9 + n\)[/tex])."
- This option correctly identifies that addition is commutative and that the phrases "a number increased by nine" and "nine increased by a number" both correctly describe the expression [tex]\( 9 + n \)[/tex]. Therefore, this option is correct.
4. Option 4: "It is incorrect. A number increased by nine refers to a multiplication expression ([tex]\(n \times 9\)[/tex])."
- This option is incorrect because "increased by" refers to addition, not multiplication. [tex]\( n \times 9 \)[/tex] means "a number multiplied by nine," not "a number increased by nine." Therefore, this option is incorrect.
Given the above analysis, the best description of the accuracy of Jillian's answer is:
It is correct. A number increased by nine ([tex]\(n + 9\)[/tex]) is the same as nine increased by a number ([tex]\(9 + n\)[/tex]).
