The solution set for the inequation -2x + 7 ≤ 3, x ∈ R is :

1. {x : x ∈ R, x < 2}

2. {x : x ∈ R, x > 2}

3. {x : x ∈ R, x ≤ 2}

4. {x : x ∈ R, x ≥ 2}

For 7 - 3x < x - 5, the solution set is :

1. x > 3

2. x < 3

3. x ≥ 3

4. x ≤ 3

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 ⇒ $\dfrac{1}{7} \lt \dfrac{1}{5}$

State, whether the following statements are true or false.

(i) If a < b, then a - c < b - c

(ii) If a > b, then a + c > b + c

(iii) If a < b, then ac > bc

(iv) If a > b, then $\dfrac{a}{c} \lt \dfrac{b}{c}$

(v) If a - c > b - d; then a + d > b + c

(vi) If a < b, and c > 0, then a - c > b - c

where a, b, c, and d are real numbers c ≠ 0.