How will \(5x-8\ge 2x+10\) be shown on the number line?

Correct answer: \(x\ge 6\), closed dot at \(6\) and shading to the right

For \(5x-8\ge 2x+10\), add \(2x\) to both sides to get \(3x-8\ge 10\). Adding \(8\) gives \(3x\ge 18\), so \(x\ge 6\). Hence, mark a closed dot at \(6\), since it is included, and shade to the right. Option A has the correct direction but an open dot, which excludes \(6\). Exam tip: use a closed dot for \(\ge\) or \(\le\), and an open dot for \(>\) or \(<\).