| I. Solution set of the inequality \[-15<\frac{3(x-2)}{5}\le 0\]is \[(-23,2]\] |
| II. Solution set of the inequality |
| \[7\le \frac{3x+11}{2}\le 11\] is \[\left[ 1,\frac{11}{3} \right]\] |
| III. Solution set of the inequality |
| \[-5\le \frac{2-3x}{4}\le 9\] is \[[-1,\,\,\,1]\cup [3,\,\,\,5]\] |
| Choose the correct option |
A) Only I and II are true.
B) Only II and III are true.
C) Only I and III are true.
D) All are true.
Correct Answer: A
Solution :
[a]| I. \[-75<3x-6\Rightarrow -23<x;\,\,3x-6\le 0\Rightarrow x\le 2\] |
| II. \[14\le 3x+11\Rightarrow 3\le 3x\Rightarrow 1\le x\] |
| \[3x+11\le 22\Rightarrow 3x\le 11\Rightarrow x\le \frac{11}{3}\] |
| III. \[-20\le 2-3x\Rightarrow x\le \frac{22}{3}\] |
| \[2-3x\le 36\Rightarrow -34\le 3x\Rightarrow x\ge \frac{-34}{3}\] |
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