State, true or false :

(i) x < -y ⇒ -x > y

(ii) -5x ≥ 15 ⇒ x ≥ -3

(iii) 2x ≤ -7 ⇒ $\dfrac{2x}{-4} \ge \dfrac{-7}{-4}$

(iv) 7 > 5 ⇒ $\dfrac{1}{7} \lt \dfrac{1}{5}$

(i) Given,

x < -y

∴ -x > y [Using rule 5]

Hence, the statement is True.

(ii) Given,

-5x ≥ 15

Dividing both sides of the above inequation by -5,

⇒ x ≤ -3 [Using rule 4]

Hence, the statement is False.

(iii) Given,

2x ≤ -7

Dividing both sides of the above inequation by -4,

⇒ $\dfrac{2x}{-4} \ge \dfrac{-7}{-4}$ [Using rule 4]

Hence, the statement is True.

(iv) Given,

7 > 5

Taking reciprocals,

$\dfrac{1}{7} \lt \dfrac{1}{5}$ [Using rule 6]

Hence, the statement is True.