To solve the inequalities, we can first find the roots of each quadratic equation.

1) For the inequality x² - 3x + 2 > 0:

To find the roots of x² - 3x + 2 = 0, we can factorize the quadratic equation:
(x - 1)(x - 2) = 0
This gives us roots x = 1 and x = 2.

The inequality x² - 3x + 2 > 0 means the quadratic is greater than zero when x is between the roots, so the solution is:
1 < x < 2

2) For the inequality x² + 5x + 6 ≤ 0:

To find the roots of x² + 5x + 6 = 0, we can factorize the quadratic equation:
(x + 2)(x + 3) = 0
This gives us roots x = -2 and x = -3.

The inequality x² + 5x + 6 ≤ 0 means the quadratic is less than or equal to zero when x is between the roots, so the solution is:
-3 ≤ x ≤ -2

Therefore, the solutions to the inequalities are:
1 < x < 2 and -3 ≤ x ≤ -2