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# Solve the inequality 6 ≤ –3(2x – 4) < 12

Question:

Solve the inequality  –3(2x – 4) < 12

Solution:

$6 \leq-3(2 x-4)<12$

$\Rightarrow 2 \leq-(2 x-4)<4$

$\Rightarrow-2 \geq 2 x-4>-4$

$\Rightarrow 4-2 \geq 2 x>4-4$

$\Rightarrow 2 \geq 2 x>0$

$\Rightarrow 1 \geq x>0$

Thus, the solution set for the given inequalityis (0, 1].