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Q.
The solution set of the inequalities $6 \leq-3(2 x-4)<12$ is
Linear Inequalities
Solution:
The given inequality $6 \leq-3(2 x-4)<12$
$6 \leq-6 x+12<12$
Adding $(-12)$ to each term,
$6-12 \leq-6 x+12-12<12-12 $
$ \Rightarrow -6 \leq-6 x<0 $
Dividing by $(-6)$ to each term,
$ \frac{-6}{-6} \geq \frac{-6 x}{-6}>\frac{0}{-6} $
$\Rightarrow 1 \geq x >0 $
$\Rightarrow 0 < x \leq 1$
$\therefore$ Solution set is $(0,1]$.