Which number-line graph is correct for \(\frac{x-1}{3}\ge 2\)?

Correct answer: Closed dot at \(7\), shaded right

Solving \(\frac{x-1}{3}\ge 2\) gives \(x-1\ge 6\), hence \(x\ge 7\). Therefore, \(7\) is included in the solution, so it is shown by a closed dot, with shading to the right for all values greater than \(7\). Option B has an open dot at \(7\), which would represent \(x>7\). Exam tip: use a closed dot for \(\ge\) or \(\le\), and an open dot for \(>\) or \(<\).