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 $\left[1,\frac{11}{3}\right]$
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.

Answer 1

Answer: (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. $-20\le 2-3x$
$\Rightarrow x\le \frac{22}{3}$
$2-3x\le 36$
$\Rightarrow -34\le 3x$
$\Rightarrow x\ge \frac{-34}{3}$