Question

Find the solution set of the following inequalities and draw the graph of their solutions sets:
`(3)/|x - 2| > 5`.

Answer 1

We have `(3)/|x - 2| > 5`
3 > 5 | x - 2 |
5 | x - 2 | < 3
| x - 2 | < `(3)/(5)`
Using property | x | < a = -a < x < a
∴ `-(3)/(5) < x - 2 < (3)/(5)`

⇒ `-(3)/(5) + 2 < x < (3)/(5) + 2`

⇒ `(7)/(5) < x < (13)/(5)`

So `(3)/|x - 2| > 5`

⇒ `{x : (7)/(5) < x < (13)/(5)}`.
The graph of this set is