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