If (x\in\mathbb{R}), which is the solution of (6-2x\ge x+9)?

Correct answer: (x\le-1)

Direct answer: option B, \(x\le-1\). Begin with \(6-2x\ge x+9\). Subtract \(x\): \(6-3x\ge9\). Subtract 6: \(-3x\ge3\). Divide by \(-3\), reversing the inequality: \(x\le-1\). Option B is correct and includes equality because the original sign is \(\ge\). Option A has the direction reversed. Option C has the wrong boundary and direction. Option D has the wrong boundary, although its direction is not the needed one either. Checking \(x=-1\) gives 8 on both sides, so the endpoint belongs. Remember: a negative divisor flips \(\ge\) into \(\le\).