Final answer:
The solution set of the inequality x^2 - 8x + 12 < 0 is found by factoring the quadratic expression to (x - 2)(x - 6) < 0, determining the intervals based on the critical values, and testing these intervals to find that the inequality is true for 2 < x < 6.
Step-by-step explanation:
To find the solution set of the inequality x^2 − 8x + 12 < 0, we first need to factor the quadratic expression. Factoring the expression, we get:
(x - 2)(x - 6) < 0
This gives us two critical values for the inequality, x = 2 and x = 6. To determine where the inequality holds true, we can test values from the intervals created by these critical points, which are (-∞, 2), (2, 6), and (6, +∞).
By testing, we find that the inequality is true for values of x between 2 and 6. So the solution set of the inequality is:
2 < x < 6
This is the range of x values for which the original inequality holds true.