What is the solution of the inequality (4-3x\ge 13)?

Correct answer: (x\le -3)

The direct answer is A: \(x\leq-3\). Start with \(4-3x\geq13\). Subtract 4 from both sides: \(-3x\geq9\). Now divide by \(-3\). When an inequality is divided by a negative number, its direction reverses, so \(x\leq-3\). Option A is exactly this result. Option B, \(x\geq-3\), forgets the reversal. Option C, \(x<-3\), incorrectly excludes equality; \(x=-3\) gives \(4-3(-3)=13\), so equality is allowed. Option D, \(x>-3\), has both the wrong direction and wrong strictness. A quick check confirms the result: choose \(x=-4\); then \(4+12=16\geq13\), so values below -3 work. Choose \(x=0\); then 4 is not at least 13, so it does not work. Memory cue: dividing an inequality by a negative flips the sign.