Select the correct answer. Which inequality represents all the solutions of -5x + 5 ≥ 160 − 10x? A. x ≤ -33 B. x ≥ 33 C. x ≥ 31 D. x ≤ 31

To solve the inequality \(-5x + 5 \geq 160 - 10x\), we will first simplify and isolate \(x\). 1. Start with the original inequality: \[ -5x + 5 \geq 160 - 10x \] 2. Add \(10x\) to both sides to get all the \(x\) terms on one side: \[ -5x + 10x + 5 \geq 160 \] This simplifies to: \[ 5x + 5 \geq 160 \] 3. Next, subtract \(5\) from both sides: \[ 5x \geq 155 \] 4. Finally, divide both sides by \(5\): \[ x \geq 31 \] Thus, the inequality that represents all the solutions is: **C. \(x \geq 31\)**