✔ 最佳答案
(1) -2 < -x < -1
Multiply by -1, we get 2 > x > 1
Ans (1) : 1 < x < 2
(2) -2 > -x > -3
Mulitply by -1, we get 2 < x < 3
Ans (2) : 2 < x < 3
(3) (x + 1)(x - 3) > 0, (x - 4)(x - 5) > 0
Remember, "Greater" on both sides, "Smaller" in the middle, so, LS is x < -1 or x > 3; and, RS is x < 4 or x >5
Ans (3) : 3 < x < 4 or x > 5
(4) (x - 3)(x + 4) < 0, (x - 1)(x + 3) >0
Same, so, LS is -4 < x < 3; and, RS is x < -3 or x > 1
Ans (4) : -4 < x < -3 or 1 < x < 3
(5) (x - 1)⁷(x + 6)²¹(2x - 5)³²(3x - 2)⁶(3x + 4)(4x² - 2x + 1) > 0
As 4x² - 2x + 1 is always greater than 0, and even power is always greater than or equal to zero, so the inequality equation becomes
(x - 1)(x + 6)(3x + 4) > 0 and x except 5/2, 2/3, so
-6 < x < -4/3 or x > 1 except 5/2, 2/3
Ans (5) : -6 < x < -4/3 or 1 < x < 5/2 or x > 5/2
(6) (x - 1)⁷(x + 6)²¹(2x - 5)³²(3x - 2)⁶(3x + 4)(4x² - 2x + 1) < 0
Same as (5), so the inequality equation becomes
(x - 1)(x + 6)(3x + 4) < 0 and x except 5/2, 2/3, so
x < -6 or -4/3 < x < 1 except 5/2, 2/3
Ans (6) : x < -6 or -4/3 < x < 2/3 or 2/3 < x < 1