Question

Solve the following inequalities and graph their solution set:
`(2x - 5)/(x + 2) < 2`

Answer 1

The inequality `(2x - 5)/(x + 2) < 2` is 

eqivalent to `(2x - 5)/(x + 2) - 2 < 0 ⇔ (2x - 5 - 2x - 4)/(x + 2) < 0`

⇒ `(-9)/(x + 2) < 0`

But `(a)/(b) < 0, a < 0`
⇒ b > 0
Thus, `(-9)/(x + 2) < 0, -9 < 0`
⇒ x > -2 > 0
⇒ x > -2
The graph of this solution is x > -2.