Question

Consider the following statements.
I. Solution set of the inequality $-15<\frac{3\left(x-2\right)}{5}\le 0$ is $(-23,2]$
II. Solution set of the inequality $7\le \frac{3x-11}{2}\le 11is\left[1,\frac{11}{3}\right]$
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)

$I.-75<3x-6\Rightarrow -23<x;\Rightarrow 3x-6\le 0\Rightarrow x\le 2$
$II.14\le 3x+11\Rightarrow 3\le 3x\Rightarrow 1\le x$
$3x+11\le 22\Rightarrow 3x\le 11\Rightarrow x\le \frac{11}{3}$
$III.-20\le 2-3x\Rightarrow x\le \frac{22}{3}$
$2-3x\le 36\Rightarrow -34\le 3x\Rightarrow x\ge \frac{-34}{3}$