MATH 121

INEQUALITIES

1.   (x + 1)(x - 1) ≥0

2.   (x - 3)(4 - x) ≥ 0

3.   (2 + 2x)(3 - x) < 0

4.   (x + 2)2(x - 1) < 0

5.   x2 + 3x > 0

6.  

7.  

8.   x2 - x > 6

9.   x2 - 2x < 3

10.   4 - x2 > 0

11.   x2 > 9

12.  

13.  

14.   (x + 1)(x - 4)(x - 3) > 0

15.   (x + 1)2(x - 4)(x - 3)3 > 0

16.   (2x + 1)(x + 3)2(x - 1)3 ≤0

17.  

18.  

19.   2 - √5x + x2< 0

20.   2x2 - 6x + 3 < 0

21.  

ANSWERS

1.   x ≥ 1 or x ≤ -1

2.   3 ≤ x ≤4

3.   x < -1 or x > 3

4.   x < 1 , x ≠ -2

5.   x < -3 or x > 0

6.   -2 < x < 1

7.   x < -2 or 3 < x < 4

8.   x < -2 or x > 3

9.   -1 < x < 3

10.   -2 < x < 2

11.   x < -3 or x > 3

12.   x < -2 or x > 1

13.   -5 ≤ x < -2

14.   x > 4 or -1 < x < 3

15.   x > 4 or x < 3 ; x ≠-1

16.   – ½ ≤ x ≤ 1 or x = -3

17.   0 < x ≤ 1 or 2 ≤ x ≤ 3

18.   x < 1 or 2 < x < 3 or x > 4

19.   ∅

20.   < x <

21.   x > or 0 < x < ½