What is the solution of the inequality (9-3x>0)?

Correct answer: (x<3)

The direct answer is A: \(x<3\). Solve step by step: \(9-3x>0\). Subtract 9 from both sides to get \(-3x>-9\). Now divide by -3. Because the divisor is negative, the inequality sign must reverse: \(x<3\). Therefore A is correct. A direct check confirms it: if x=2, then \(9-3(2)=3>0\). Option B, \(x>3\), has the reversed direction and fails for x=4, giving \(9-12=-3>0\), which is false. Option C, \(x\le3\), incorrectly includes x=3; at x=3 the expression is 0, and 0>0 is false. Option D, \(x\ge3\), also includes the invalid boundary and values above it. The strict sign > means equality is not allowed. The key rule is that multiplying or dividing by a negative number reverses the inequality. Memory cue: “negative crossing flips the sign.”