Answer
The match is as follow:
(a) - (i)
(b) - (iii)
(c) - (v)
(d) - (vi)
(e) - (ii)
(f) - (iv)
Work Step by Step
(a) a > 3, this implies that the value of a is greater than 3. So, a simply lies on the right side of 3 in the graph. Hence,option (i).
(b) |a-5| < 1/3
modules of 'a-5' represents the positive value and in graphs we read it as distance between 'a' and 5. Therefore, this statement means the distance between 'a' and 5 is less than 1/3. Hence, option (iii) matches with explanation.
(c) |a - 1/3| < 5.
As from the part (b), modules of 'a' and 1/3 represents the distance between 'a' and 1/3 which is less than 5 units. So, option (v) matches here.
(d) |a| > 5,
removing the modules: a > 5 or a < -5. From here we can see 'a' is greater than 5 and less than -5. So, 'a' either lies on the right of 5 or left side of the -5 in the graph. Hence, option (vi).
(e) |a - 4| < 3
removing the modules:
a - 4 < 3 or a - 4 >-3
in case 1: a-4<3, taking 4 on the right side
a<7 and in case 2: a-4>-3, taking 4 on the right side
a>1. So, combining both will give us 1
