Polynomial and Rational Inequalities - Questions and Answers

Questions on solving Polynomial and Rational Inequalities are presented. These may be used as a self test. Answers to the questions are also provided.

You have 10 questions on this page and the same questions in the applet below. You may want to go through a tutorial on inequalities first.

Inequalities questions with answers

Question 1: Solve the inequality.

-(x + 2) + 2x > 2(x - 3) + 3x


a: no solutions

b: (-infinity , 4/5)

c: (4/5 , +infinity)

d: (-infinity , +infinity)

e: (-infinity , 1)

Question 2: Solve the polynomial inequality.

(6x + 2) (10 - 20x) > = 0


a: (-1/3 , 1/2)

b: [-1/2 , +infinity)

c: no solutions

d: (-infinity , 0]

e: [-1/3 , 1/2]

Question 3: Solve the inequality.

x2 + 3x - 4 > 0


a: (-4 , 1)

b: (-infinity , -4) U (1 , +infinity)

c: (1 , +infinity)

d: no solutions

e: (-infinity , -4] U [1 , +infinity)

Question 4: Solve the inequality.

2x2 < 32


a: (-4 , 4)

b: (-infinity , 4)

c: (-sqrt(32) , sqrt(32))

d: no solutions

e: (-4 , +infinity)

Question 5: Solve the inequality.

25x2 <= 9x


a: no solutions

b: (-infinity , +infinity)

c: [0 , +infinity)

d: [0 , 9/25]

e: [0 , 9/5)

Question 6: Solve the inequality.

(1 + x) / |x - 2| > 0


a: (-1 , +infinity)

b: (-1 , 2) U (2 , +infinity)

c: [-1 , +infinity)

d: (2 , +infinity)

e: (-infinity , +infinity)

Question 7: Solve the inequality.

(2x2 + 3) (x + 2) / (x2 - 4) > = 0


a: (-infinity , +infinity)

b: (-infinity , 2)

c: (2, +infinity)

d: [2, +infinity)

e: no solutions

Question 8: Solve the inequality.

4 / (6x - 4) < = 2 / (2x + 2)


a: (-infinity , -1] U [4 , +infinity)

b: (2/3 , 4]

c: (-1 , 2/3)

d: (-1 , 2/3) U [4 , +infinity)

e: [ 4, +infinity)

Question 9: Solve the inequality.

2 < |x + 1| / 2 - 2 < 5


a: (-3, -15)

b: no solutions

c: (-15, -9) U (7 , 13)

d: (7 , 13)

e: (-infinity , +infinity)

Question 10: Solve the inequality.

x2 < -x4


a: no solutions

b: (-1 , 1)

c: (-infinity , +infinity)

d: (0 , +infinity)

e: [0 , +infinity)

Inequalities questions with answersapplet

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More references and links to math questions.

Math Problems, Questions and Online Self Tests.

Solve Inequalities in One Variable