Final answer:
Option D (Adding 10 to both sides) is the correct action that would NOT change the solution set of the equation x + 7 = 14. Other options, which are subtracting 7, dividing by 2, and multiplying by 3, maintain the solution set by preserving the equality.
Step-by-step explanation:
The student is asking which action would NOT change the solution set of the equation x + 7 = 14. The options provided are A) Subtracting 7 from both sides, B) Dividing both sides by 2, C) Multiplying both sides by 3, and D) Adding 10 to both sides.
When solving for x in the given equation, the goal is to isolate x on one side of the equation:
- Option A: Subtracting 7 from both sides results in x = 7. This maintains the solution set because it preserves the equality by performing the same operation on both sides.
- Option B: Dividing both sides by 2 gives (x + 7)/2 = 7. This also maintains the solution set but with a transformed equation.
- Option C: Multiplying both sides by 3 yields 3(x + 7) = 42. This action does not change the solution set; it just scales the equation.
- Option D: Adding 10 to both sides results in x + 17 = 24, which changes the solution set as it doesn't maintain the equality between both sides of the equation.
Thus, the correct answer is D) Adding 10 to both sides, as this action would change the solution set of the equation while the other options would not.