Equations And Inequalities Question 22
Question: Consider the following statements.
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 $ [ 1,\frac{11}{3} ] $
III. Solution set of the inequality
$ -5\le \frac{2-3x}{4}\le 9 $ is $ [-1,,1]\cup [3,,5] $
Choose the correct option
Options:
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.
Show Answer
Answer:
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} $
BETA
