Given Inequality:
\(6 \le -3(2x - 4) < 12\)
Step 1: Expand the expression
\(-3(2x - 4) = -6x + 12\)
So the inequality becomes:
\(6 \le -6x + 12 < 12\)
Step 2: Subtract 12 from all parts
\(-6 \le -6x < 0\)
Step 3: Divide all parts by −6
(Note: Dividing by a negative number reverses the inequality signs)
\(1 \ge x > 0\)
Rewriting in standard form:
\(0 < x \le 1\)
Graphical Representation on Number Line:
An open circle at 0 and a closed circle at 1,
with the region between 0 and 1 shaded.
Final Answer:
The solution set is
{ x ∣ 0 < x ≤ 1 }