Question

Solve the following linear inequations:

(i) 4x – 12 < 0 

(ii) – 5x + 10 < 0 

(iii) 7x – 35 > 0 

(iv) 11x + 9 > 53, where x∈W

Answer 1

(i) 4x – 12 < 0 ⇒ 4x < 12 ⇒ x < 3 

∴ Solution set of given inequation is (─ ∞, 3] 

(ii) –5x + 10 < 0 ⇒ –5x < – 10 

⇒ \(\frac{-5x}{-5}>\frac{-10}{-5}\) [∵ Dividing both sides of an inequality by a negative number reverses the inequality] 

⇒ x > 2 ⇒ Solution set is (2, ∞) 

(iii) 7x – 35 > 0 ⇒ 7x > 35 ⇒ x > 5 ⇒ Solution set is [5, ∞) 

(iv) 11x + 9 > 53 ⇒ 11x > 44 ⇒ x > 4    ∴ Solution set is (4, ∞)