Solve the inequality (2 - x)(x + 3) > 0. Which of the following is the solution set?
Show the answer and explanation
Correct answer
A. (-3, 2)
Principle or equation
For a quadratic inequality of the form a(x - r1)(x - r2) > 0 with a < 0, the solution is the interval between the roots. Here the roots are -3 and 2, and the leading coefficient is negative, so the expression is positive between the roots.
Why this answer is correct
The inequality (2 - x)(x + 3) > 0 has roots x = 2 and x = -3. The coefficient of x^2 is -1, so the parabola opens downward. Thus the expression is positive for x between -3 and 2. The solution is (-3, 2).
Example
For (1 - x)(x + 2) > 0, roots are -2 and 1, leading coefficient negative, so solution is (-2, 1).
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