To solve the inequality, we first need to solve the equation x^2 - 5x + 6 = 0 by factoring or using the quadratic formula.
x^2 - 5x + 6 = (x - 2)(x - 3) = 0 This gives us x = 2 and x = 3 as the solutions to the equation.
Now we need to determine the intervals where the inequality |x-2| < 3 holds. The inequality |x-2| < 3 can be rewritten as -3 < x - 2 < 3, which simplifies to -1 < x < 5.
Therefore, the solutions to the inequality x^2 - 5x + 6 > 0 are x ∈ (-1, 2) ∪ (3, 5).
To solve the inequality, we first need to solve the equation x^2 - 5x + 6 = 0 by factoring or using the quadratic formula.
x^2 - 5x + 6 = (x - 2)(x - 3) = 0
This gives us x = 2 and x = 3 as the solutions to the equation.
Now we need to determine the intervals where the inequality |x-2| < 3 holds. The inequality |x-2| < 3 can be rewritten as -3 < x - 2 < 3, which simplifies to -1 < x < 5.
Therefore, the solutions to the inequality x^2 - 5x + 6 > 0 are x ∈ (-1, 2) ∪ (3, 5).