AlgebraVery hardParameter that reverses an inequality's solution set
Algebra practice question
For which values of the constant k is the solution set of kx + 3 > 3 exactly the set of all x less than 0?
- A. k < 0Correct
- B. k > 0
- C. k = 0
- D. k > 3
Answer: A. k < 0
kx + 3 > 3 means kx > 0. That holds for exactly the negative x when k is negative (dividing by k flips the inequality).
Why the other answers are wrong
- B. k > 0
- For k > 0 the solutions are x > 0.
- C. k = 0
- For k = 0 the inequality is 3 > 3, never true.
- D. k > 3
- k > 3 is a subset of k > 0, which gives the wrong set.
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