Question

Match List I with List II

	LIST I		LIST II
A.	The solution set of the inequality  \(-5x > 3, x\in R\), is	I.	\([\frac{20}{7},∞)\)
B.	The solution set of the inequality is, \(\frac{-7x}{4} ≤ -5, x\in R\) is,	II.	\([\frac{4}{7},∞)\)
C.	The solution set of the inequality \(7x-4≥0, x\in R\) is,	III.	\((-∞,\frac{7}{5})\)
D.	The solution set of the inequality \(9x-4 < 4x+3, x\in R\) is,	IV.	\((-∞,-\frac{3}{5})\)

Choose the correct answer from the options given below:

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

Answer 1

The Correct Option is A

To solve the problem of matching List I with List II, we'll assess which solution set corresponds to each inequality in List I.

1. A. The inequality is \( -5x > 3 \). Solving for \( x \):

   \(-5x > 3 \\ x < -\frac{3}{5}\)

   The solution set is \(x \in (-\infty,-\frac{3}{5})\), corresponding to IV.

2. B. The inequality is \(\frac{-7x}{4} \leq -5\). Solving for \( x \):

   \(\frac{-7x}{4} \leq -5 \\ -7x \leq -20 \\ x \geq \frac{20}{7}\)

   The solution set is \(x \in [\frac{20}{7},\infty)\), corresponding to I.

3. C. The inequality is \( 7x - 4 \geq 0 \). Solving for \( x \):

   \(7x \geq 4 \\ x \geq \frac{4}{7}\)

   The solution set is \(x \in [\frac{4}{7},\infty)\), corresponding to II.

4. D. The inequality is \(9x - 4 < 4x + 3\). Solving for \( x \):

   \(5x < 7 \\ x < \frac{7}{5}\)

   The solution set is \(x \in (-\infty,\frac{7}{5})\), corresponding to III.

Thus, the correct matches are:

• (A) – (IV)
• (B) – (I)
• (C) – (II)
• (D) – (III)

The correct answer from the options provided is:

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