Given Inequality:
\( 37 - (3x + 5) \ge 9x - 8(x - 3) \)
Step 1: Simplify both sides
Left-hand side:
\( 37 - 3x - 5 = 32 - 3x \)
Right-hand side:
\( 9x - 8(x - 3) = 9x - 8x + 24 = x + 24 \)
Step 2: Form the inequality
\( 32 - 3x \ge x + 24 \)
Step 3: Solve the inequality
\( 32 - 24 \ge x + 3x \)
\( 8 \ge 4x \)
\( x \le 2 \)
Graphical Representation on Number Line:
A closed circle at 2 and the region to the left of 2 is shaded.
Final Answer:
The solution set is
{ x ∣ x ≤ 2 }