Final answer:
The factors of 18 that sum to -7 are -9 and 2. After finding the pair, it was verified that both are factors of 18 and their sum is -7, which aligns with the requested sum.
Step-by-step explanation:
The student asked to identify the factors of 18 that will give a sum of -7. The factors of 18 are 1, 2, 3, 6, 9, and 18. To find a combination of these factors which sum to -7, we must include negative numbers, since the sum required is negative. The only pair of factors from this list that add up to -7 are -9 and 2, because -9 + 2 = -7.
To check if our answer is reasonable, we verify that both -9 and 2 are indeed factors of 18 (-9 x -2 = 18), and that their sum matches the requested sum (-9 + 2 = -7). This demonstrates the importance of elimination and checking in simplifying algebra.