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