Match the LIST-I with LIST-II
| LIST-I | LIST-II |
| Inequality | Solution set |
| A. \( 4x+3\le 6x+7 \) | I. \( x\in(-\infty,-2) \) |
| B. \( 5x-5\gt 3x-1 \) | II. \( x\in(-\infty,2] \) |
| C. \( 4x-9\gt 6x-5 \) | III. \( x\in[-2,\infty) \) |
| D. \( 3x-1\le 5 \) | IV. \( x\in(2,\infty) \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-III, B-IV, C-I, D-II
Each inequality is solved by collecting the x terms on one side. Dividing by a negative number reverses the inequality.
(A) \( 4x+3\le 6x+7 \)
This matches III.
\( -4\le 2x \)
\( x\ge -2 \)
(B) \( 5x-5\gt 3x-1 \)
This matches IV.
\( 2x\gt 4 \)
\( x\gt 2 \)
(C) \( 4x-9\gt 6x-5 \)
This matches I. Dividing by −2 reverses the sign:
\( -2x\gt 4 \)
\( x\lt -2 \)
(D) \( 3x-1\le 5 \)
This matches II.
\( 3x\le 6 \)
\( x\le 2 \)
So the matching is A-III, B-IV, C-I, D-II.