Match List-I with List-II
| List-I | List-II | ||
| (A) | The solution set of the inequation \( 3x-6\le 0 \) is | (I) | \( (3,\infty) \) |
| (B) | The solution set of the inequation \( -5x+20\lt 0 \) is | (II) | \( [3,\infty) \) |
| (C) | The solution set of the inequation \( 3x-9\ge 0 \) is | (III) | \( (-\infty,2] \) |
| (D) | The solution set of the inequation \( 8x+11\gt 35 \) is | (IV) | \( (4,\infty) \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) - (III), (B) - (IV), (C) - (II), (D) - (I)
(A) The solution set of the inequation \( 3x-6\le 0 \) is
This matches (III) \( (-\infty,2] \).
\( \displaystyle 3x\le 6\ \Rightarrow\ x\le 2 \)
(B) The solution set of the inequation \( -5x+20\lt 0 \) is
This matches (IV) \( (4,\infty) \).
Dividing by −5 reverses the inequality:
\( \displaystyle -5x\lt -20\ \Rightarrow\ x\gt 4 \)
(C) The solution set of the inequation \( 3x-9\ge 0 \) is
This matches (II) \( [3,\infty) \).
\( \displaystyle 3x\ge 9\ \Rightarrow\ x\ge 3 \)
The end point 3 is included, so the bracket is square.
(D) The solution set of the inequation \( 8x+11\gt 35 \) is
This matches (I) \( (3,\infty) \).
\( \displaystyle 8x\gt 24\ \Rightarrow\ x\gt 3 \)
The end point 3 is excluded, so the bracket is round.
So the matching is (A)-(III), (B)-(IV), (C)-(II), (D)-(I).