rohan_vus wrote:Brent Hanneson wrote:Resurgent wrote:Which of the following is correct if x is a real number and (x - 11)(x - 3) is negative?
A. x^2 + 5x + 6 < 0
B. x^2 + 5x + 6 > 0
C. 5 - x < 0
D. x - 5 < 0
E. 11 - x > 0
PS: I do not have the OA for this question.
Here's my solution. It includes a systematic way to solve quadratic inequalities.
The answer is not E since one solution to E is x=0 and x=0 is not a solution to the original inequality.
With respect to the logic behind bold statement , one solution is x = -4 which satisfies option B but its not a solution to original inequality . This question seems kinda odd to me
In our answer choices, we are looking for an inequality such that every possible value for x from the original inequality [ (x-11)(x-3) < 0 ] must also be a solution to the inequality among the answer choices. You are ready the question the other way around.
x = -4 is not a solution to the original inequality (x-11)(x-3) < 0, so we need not consider that value for x when checking the answer choices. We need only consider values of x between 3 and 11.
When we plug these allowable values into the inquality in answer choice B, EVERY value of x is such that x^2 + 5x + 6 > 0
The same cannot be said for the other answer choices.
