What is the solution of (-3(x+2)+7\ge 2(4-x)-5)?

Correct answer: \(x\le -2\)

Simplifying the left side gives \(-3(x+2)+7=-3x+1\), and simplifying the right side gives \(2(4-x)-5=3-2x\). Thus, \(-3x+1\ge 3-2x\), which gives \(-x\ge 2\), and hence \(x\le -2\). The option \(x<-2\) is close, but at \(x=-2\) both sides are equal, so \(-2\) must be included. Exam tip: reverse the inequality sign whenever you multiply or divide an inequality by a negative number.