1)(x-1)(x+1) ≤ 0(x-1)(x+1) = 0 when x = 1 or x = -1So, the solution set is -1 ≤ x ≤ 1
2)-x² - 5x + 6 > 0(x-2)(x-3) > 0This quadratic is positive when x < 2 or x > 3So, the solution set is x < 2 or x > 3
3)2 + x - x² ≥ 0-x² + x + 2 ≥ 0-(x-2)(x+1) ≥ 0This quadratic is positive when -1 ≤ x ≤ 2So, the solution set is -1 ≤ x ≤ 2
4)3x² - 7x + 2 < 0(3x-1)(x-2) < 0This quadratic is negative when 1/3 < x < 2So, the solution set is 1/3 < x < 2
1)
(x-1)(x+1) ≤ 0
(x-1)(x+1) = 0 when x = 1 or x = -1
So, the solution set is -1 ≤ x ≤ 1
2)
-x² - 5x + 6 > 0
(x-2)(x-3) > 0
This quadratic is positive when x < 2 or x > 3
So, the solution set is x < 2 or x > 3
3)
2 + x - x² ≥ 0
-x² + x + 2 ≥ 0
-(x-2)(x+1) ≥ 0
This quadratic is positive when -1 ≤ x ≤ 2
So, the solution set is -1 ≤ x ≤ 2
4)
3x² - 7x + 2 < 0
(3x-1)(x-2) < 0
This quadratic is negative when 1/3 < x < 2
So, the solution set is 1/3 < x < 2