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Question
Solve the following inequalities and graph their solution set:
`(x + 8)/(x + 1) > 1`.
Solution
The inequality `(x + 8)/(x + 1) > 1` is equivalent to
`(x + 8)/(x + 1) - 1 > 0 ⇔ (x + 8 - x - 1)/(x + 1) > 0`
⇒ `(7)/(x + 1)`
= 0
but `(a)/(b) > 0, a > 0 ⇔ b > 0`
Thus, `(7)/(x + 1) > 0, 7 > 0`
⇒ x + 1 > 0 or x > -1
The graph of this set is
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