Question

Consider the following statements.
I. Solution set of the inequality $-15 < \frac{3\left(x-2\right)}{5} \le0$ 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 $\left[-1, 1\right]\cup\left[3, 5\right]$
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

Answer 1

Answer: (A)

$I.-75 < 3x-6 \Rightarrow -23 < x; \Rightarrow 3x-6 \le0 \Rightarrow x \le2$
$II. 14 \le3x+11 \Rightarrow 3 \le3x \Rightarrow 1 \le x$
$3x+11\le22 \Rightarrow 3x \le11 \Rightarrow x \le \frac{11}{3}$
$III. -20 \le2-3x \Rightarrow x \le\frac{22}{3}$
$2-3x \le36 \Rightarrow -34 \le3x \Rightarrow x \ge \frac{-34}{3}$