What is the solution of (2(1-3x)\le 5-4(2x+1))?

Correct answer: \(x\le-\frac{1}{2}\)

Expanding the left-hand side gives \(2(1-3x)=2-6x\), and expanding the right-hand side gives \(5-4(2x+1)=1-8x\). Thus, \(2-6x\le1-8x\). Adding \(8x\) to both sides gives \(2+2x\le1\), so \(2x\le-1\). Dividing by 2 gives \(x\le-\frac{1}{2}\). The option \(x\ge-\frac{1}{2}\) is incorrect because no division or multiplication by a negative number occurs, so the inequality sign does not reverse. Exam tip: reverse an inequality sign only when multiplying or dividing by a negative number.