Question 18: is the solution set of and is the solutions et of ; where . Represent i) ii) iii) on different number lines.

Answer:

Question 19: If and ; find the range of the set P \cap Q and represent it on number line.

Answer:

Question 20: Find the range of values of x, which satisfy: Graph in each of the following cases for the values of x for each of the following cases: i) ii) iii)

Answer:

i) :

ii) :

iii) :

Question 21: Given , where is real numbers and is integers. Represent on two different number lines. Also write down the elements of .

Answer:

Question 22: Solve the following inequation and graph the solution on a number line , where . [2011]

Answer:

or

Therefore

Question 23: Given that , solve the inequation and graph it on a number line: . [2004]

Answer:

Therefore

Question 24: Given , . Find the range of the set and represent it on a number line. [2005]

Answer:

Question 25: Find the set of values of , satisfying: and , where .

Answer:

Therefore

Question 26: Solve i) , where is a positive odd integer. ii) , where is a positive even integer.

Answer:

i)

ii)

Question 27: Solve the inequation: . Graph the solution on a number line.

Answer:

Therefore

Question 28: Find three consecutive largest positive integers such that the sum of one third of the first, one fourth of the second and one fifth of the third is 20.

Answer:

Let the three numbers be

Therefore

Hence . Therefore the numbers are .

Question 29: Solve the given inequation and graph it on a number line: . [2008]

Answer:

Hence

Question 30: Solve the inequation: . Graph the solution set on a number line.

Answer:

or

Hence

Question 31: Solve the given inequation and graph it on a number line: . [2010]

Answer:

Therefore

Question 32: Solve the given inequation and graph it on a number line: . [2012]

Answer:

Therefore

Question 33: Solve the given inequation and graph it on a number line: . [2013]

Answer:

or

Therefore

Question 34: Find the value of which satisfies the inequation: . [2014]

Answer:

Therefore