Question

Consider the following statements.
I. Solution set of the inequality $-15 < \frac{3( x -2)}{5} \leq 0$ is $(-23,2]$
II. Solution set of the inequality $7 \leq \frac{3 x+11}{2} \leq 11$ is $\left[1, \frac{11}{3}\right]$
III. Solution set of the inequality $-5 \leq \frac{2 - 3x}{4}\leq 9$ 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. $-75 < 3 x-6 \Rightarrow -23 < x$
$3 x-6 \leq 0 \Rightarrow x \leq 2$
II. $14 \leq 3 x+11 $
$\Rightarrow 3 \leq 3 x $
$\Rightarrow 1 \leq x$
$3 x+11 \leq 22 $
$\Rightarrow 3 x \leq 11 $
$\Rightarrow x \leq \frac{11}{3}$
III. $-20 \leq 2-3 x $
$\Rightarrow x \leq \frac{22}{3}$
$2-3 x \leq 36 $
$\Rightarrow -34 \leq 3 x $
$\Rightarrow x \geq \frac{-34}{3}$