Question

The solution set of the inequality \[ 37 - (3x + 5) \geq 9x - 8(x - 3) { is:} \]

• A. \( (-\infty, 2) \)
• B. \( (-\infty, -2) \)
• C. \( (-\infty, 2] \)
• D. \( (-\infty, -2] \)

Hint:

When solving inequalities, always isolate the variable on one side and simplify terms systematically.

Answer 1

The Correct Option is C

Step 1: First, simplify the inequality: \[ 37 - (3x + 5) \geq 9x - 8(x - 3). \] Distribute the terms: \[ 37 - 3x - 5 \geq 9x - 8x + 24. \] Step 2: Simplify both sides: \[ 32 - 3x \geq x + 24. \] Step 3: Move all terms involving \( x \) to one side and constants to the other side: \[ 32 - 24 \geq x + 3x \quad \Rightarrow \quad 8 \geq 4x. \] Step 4: Solve for \( x \): \[ x \leq 2. \] Thus, the solution set is \( (-\infty, 2] \).