Question

Lin is solving the inequality 15 - x < 14. She knows the solution to the equation 15 - x = 14 is x = 1. Complete the following to explain how Lin can determine whether x > 1 or x < 1 is the solution to the inequality.

a) Lin can substitute a number greater than 1 into the inequality and see if it is true. If it is true, then the solution is x > 1.
b) Lin can substitute a number less than 1 into the inequality and see if it is true. If it is true, then the solution is x < 1.
c) Lin can substitute any number into the inequality, and if it is true, it means both x > 1 and x < 1 are solutions.
d) Lin cannot determine whether x > 1 or x < 1 is the solution with this method.

Answer 1

Lin can determine whether x > 1 or x < 1 is the solution by substituting different numbers into the inequality and checking if they satisfy the inequality.

Step-by-step explanation:

In order to determine whether x > 1 or x < 1 is the solution to the inequality 15 - x < 14, Lin can follow these steps:

1. Lin can substitute a number greater than 1 into the inequality and see if it is true. If it is true, then the solution is x > 1.
2. Lin can substitute a number less than 1 into the inequality and see if it is true. If it is true, then the solution is x < 1.

Therefore, Lin can determine whether x > 1 or x < 1 is the solution by substituting different numbers into the inequality and checking if they satisfy the inequality.