Final answer:
Lin can use the inequality 15 - x < 14 to determine the solution. Since the equation 15 - x = 14 leads to x = 1, any value greater than 1 for x would make the expression smaller than 14, leading to x > 1 as the solution.
Step-by-step explanation:
Lin is solving the inequality 15 - x < 14. Since she knows that the equation 15 - x = 14 has the solution x = 1, she can determine whether x > 1 or x < 1 is the solution to the inequality using the following reasoning:
Answer choice A suggests substituting x = 1 into the inequality. However, this will only show that the equality holds, but not if other values of x make the inequality true. So, A is not the best method.
Option B suggests graphing the inequality, which can be helpful to visualize solutions, but is not necessary in this simple case.
Option C implies comparing 15 - x to 14 using the appropriate inequality symbol. Since 15 - x needs to be less than 14, and since x = 1 makes the expression equal to 14, we can conclude that for the expression to be less than 14, x must be greater than 1. So, the solution set would include all values of x that are greater than 1.
Finally, option D talks about solving for x in both cases, but we only need to consider the inequality and not solve it as two separate cases.
The correct way to determine if x is greater than or less than 1 is to use the inequality 15 - x < 14 directly, understanding that since we subtract x from 15, the larger the x, the smaller the result is. Therefore, logically, x > 1 is the solution because the expression must stay less than 14.