Given Inequality:
\(-15 < \frac{3(x-2)}{5} \le 0\)
Step 1: Multiply all parts by 5
\(-75 < 3(x-2) \le 0\)
Step 2: Divide all parts by 3
\(-25 < x-2 \le 0\)
Step 3: Add 2 to all parts
\(-23 < x \le 2\)
Graphical Representation on Number Line:
An open circle at −23 and a closed circle at 2,
with the region between −23 and 2 shaded.
Final Answer:
The solution set is
{ x ∣ −23 < x ≤ 2 }