Answer:
x = ±2, 3 are the critical points of the given inequality.
Step-by-step explanation:
The given inequality is
To find the critical points we will equate the numerator and denominator of the inequality to zero.
For numerator,
(x - 2)(x + 2) = 0
x = ±2
For denominator,
x² - 5x + 6 = 0
x² - 3x -2x + 6 = 0
x(x - 3) -2(x - 3) = 0
(x - 3)(x - 2) = 0
x = 2, 3
Therefore, critical points of the inequality are x = ±2, 3 where the sign of the inequality will change.
Choice A is the answer which is the point (1,-1)
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How I got this answer:
Plug each point into the inequality. If you get a true statement after simplifying, then that point is in the solution set and therefore a solution. Otherwise, it's not a solution.
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checking choice A
plug in (x,y) = (1,-1)
This is true because -3 is equal to itself. So this is the answer.
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checking choice B
plug in (x,y) = (2,4)
This is false because 0 is not to the left of -3, nor is 0 equal to -3. We can cross this off the list.
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checking choice C
plug in (x,y) = (-2,3)
This is false because 7 is not to the left of -3, nor is 7 equal to -3. We can cross this off the list.
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checking choice D
plug in (x,y) = (3,4)
This is false because -2 is not to the left of -3, nor is -2 equal to -3. We can cross this off the list.
