Question

Solve the following linear inequations in R

(x-1)/(x+3) > 2

\(\frac{x-1}{x+3}\) > 2

Answer 1

Given,

(x-1)/(x+3) > 2

For this inequation to be true,

There are two possible cases. 

i. x + 7 > 0 and x + 3 < 0 

⇒ x + 7 – 7 > 0 – 7 and 

x + 3 – 3 < 0 – 3 

⇒ x > –7 and x < –3 

∴ x ∈ (–7, ∞) ∩ (–∞, –3) 

However, 

(–7, ∞) ∩ (–∞, –3) = (–7, –3) 

Hence, 

x ∈ (–7, –3) 

ii. x + 7 < 0 and x + 3 > 0 

⇒ x + 7 – 7 < 0 – 7 and 

x + 3 – 3 > 0 – 3 

⇒ x < –7 and x > –3 

∴ x ∈ (–∞, –7) ∩ (–3, ∞) 

However, 

(–∞, –7) ∩ (–3, ∞) = ∅ 

Hence, 

This case is not possible. 

Thus, 

The solution of the given inequation is (–7, –3).