Question

Lin is solving the inequality 15 - x < 14. She knows the solution to the equation 15 - x = 14 is x = 1. How can Lin determine whether x > 1 or x < 1 is the solution to the inequality?

a) x > 1 is the solution.
b) x < 1 is the solution.
c) x = 1 is the only solution.
d) Lin cannot determine the solution based on the given information.

Answer 1

Lin is solving the inequality 15 - x < 14. Knowing that x = 1 is a solution to the equation 15 - x = 14, we can determine that x must be less than 1 to satisfy the inequality, so x < 1 is the solution.

Lin is solving the inequality 15 - x < 14. Given that she knows the solution to the equation 15 - x = 14 is x = 1, we must find whether x > 1 or x < 1 is the solution to the inequality. To determine this, we look at the inequality 15 - x < 14 again and consider x = 1. If we replace x with any number greater than 1, the result will be less than 14, which would not satisfy this inequality. Conversely, if we replace x with any number less than 1, the result on the left side of the inequality becomes greater than 14, which satisfies the inequality. Therefore, we can conclude that the answer is b) x < 1 is the solution.