Question

Solve `(x - 2)/(x + 5) > 2`.

Answer 1

We have,  `(x - 2)/(x + 5) > 2`

⇒ `(x - 2)/(x + 5) - 2 > 0`  .......[Subtracting 2 from each side]

⇒ `(-(x + 12))/(x + 5) > 0`

⇒ `(x + 12)/(x + 5) < 0`   .......(Multiplying both sides by –1)

⇒ x + 12 > 0 and x + 5 < 0   .....[Since `a/b < 0` ⇒ a and b are of opposite signs.]

or

x + 12 < 0 and x + 5 > 0

⇒ x > –12 and x < –5

or 

x < –12 and x > –5   .....(Not possible)

Therefore, –12 < x < –5 i.e. x ∈ (–12, –5).