Given Inequality:
\(-12 < 4 - \frac{3x}{-5} \le 2\)
Note that
\(4 - \frac{3x}{-5} = 4 + \frac{3x}{5}\)
Step 1: Rewrite the inequality
\(-12 < 4 + \frac{3x}{5} \le 2\)
Step 2: Subtract 4 from all parts
\(-16 < \frac{3x}{5} \le -2\)
Step 3: Multiply all parts by 5
\(-80 < 3x \le -10\)
Step 4: Divide all parts by 3
\(-\frac{80}{3} < x \le -\frac{10}{3}\)
Graphical Representation on Number Line:
An open circle at −80/3 and a closed circle at −10/3,
with the region between them shaded.
Final Answer:
The solution set is
{ x ∣ −80/3 < x ≤ −10/3 }