Question

Consider the solution to the system of inequalities below:

0.5x + 2
v > 3x - 3
Which of the following functions could be added to the system without changing the solution set?
A) y > 2
B) y < 3
C) y < 2
D) y = 3

Answer 1

To keep the solution set the same, we must choose a function that does not affect the inequality. The only function that could be added without changing the solution set is y > 2.

Step-by-step explanation:

To determine which function could be added to the system without changing the solution set, we need to consider the inequality 0.5x + 2v > 3x - 3. To keep the solution set the same, we must choose a function that does not affect the inequality. Let's analyze each option:

1. A) y > 2: Adding this function would not change the inequality.
2. B) y < 3: Adding this function would change the inequality to 0.5x + 2v > 3x - 3 and y < 3. It would affect the solution set.
3. C) y < 2: Adding this function would change the inequality to 0.5x + 2v > 3x - 3 and y < 2. It would affect the solution set.
4. D) y = 3: Adding this function would change the inequality to 0.5x + 2v > 3x - 3 and y = 3. It would affect the solution set.

Therefore, the only function that could be added without changing the solution set is A) y > 2.