Given Inequality:
\( -3 \le 4 - \frac{7x}{2} \le 18 \)
Step 1: Subtract 4 from all parts
\( -7 \le -\frac{7x}{2} \le 14 \)
Step 2: Multiply all parts by 2
\( -14 \le -7x \le 28 \)
Step 3: Divide all parts by −7
(Recall that dividing by a negative number reverses the inequality signs)
\( 2 \ge x \ge -4 \)
Rewriting in standard form:
\( -4 \le x \le 2 \)
Graphical Representation on Number Line:
Closed circles at −4 and 2,
with the region between −4 and 2 shaded.
Final Answer:
The solution set is
{ x ∣ −4 ≤ x ≤ 2 }