If Z and R denote set of integers and set of real numbers respectively, then match List I with List II.

Choose the correct answer from the options given below:

(A)-(III), (B)-(I), (C)-(II), (D)-(IV)

The correct answer is Option (3) → (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

Matching List-I with List-II with solutions:

(A) $5x - 3 < 3x + 1$, $x \in \mathbb{Z}$

Simplify: $5x - 3 < 3x + 1 \Rightarrow 2x < 4 \Rightarrow x < 2$

Integer solutions: $\{..., -4, -3, -2, -1, 0, 1\}$ → (III)

(B) $3x + 17 \le 2(1 - x)$, $x \in \mathbb{R}$

$3x + 17 \le 2 - 2x \Rightarrow 5x \le -15 \Rightarrow x \le -3$ → (I)

(C) $13x + 17 < 2(1 - x)$, $x \in \mathbb{R}$

$13x + 17 < 2 - 2x \Rightarrow 15x < -15 \Rightarrow x < -1$ → (II)

(D) $(2x + 3)/5 - 2 > 3(x - 2)/5$, $x \in \mathbb{Z}$

Simplify: $(2x + 3)/5 - 2 > (3x - 6)/5 \Rightarrow (2x + 3 - 10) > 3x - 6 \Rightarrow 2x - 7 > 3x - 6 \Rightarrow -x > 1 \Rightarrow x < -1$

Integer solutions: $\{..., -4, -3, -2\}$ → (IV)