Question

The solution set of the inequalities $6\le -3(2x-4)<12$ is

• A. $(-\infty ,1]$
• B. $(0,1]$
• C. $(0,1]\cup [1,\infty )$
• D. $[1,\infty )$

Answer 1

Answer: (B)

The given inequality $6\le -3(2x-4)<12$
$6\le -6x+12<12$
Adding $(-12)$ to each term,
$6-12\le -6x+12-12<12-12$
$\Rightarrow -6\le -6x<0$
Dividing by $(-6)$ to each term,
$\frac{-6}{-6}\ge \frac{-6x}{-6}>\frac{0}{-6}$
$\Rightarrow 1\ge x>0$
$\Rightarrow 0<x\le 1$
$\therefore$ Solution set is $(0,1]$.