What is the solution of the inequality (x-4\le 9)?

Correct answer: (x\le 13)

The direct answer is A: \(x\le13\). Begin with \(x-4\le9\). To remove -4 from the left side, add 4 to both sides: \(x-4+4\le9+4\). This simplifies to \(x\le13\). Addition preserves the direction of an inequality, so the symbol does not change. Option A is correct and includes x=13 because the original sign is \(\le\). Option B, \(x\ge13\), reverses the relation and would include values larger than 13, which do not work; for x=14, the original statement becomes 10\le9, false. Option C, \(x<13\), wrongly excludes x=13, which actually gives 9\le9. Option D, \(x>13\), is also the wrong direction and excludes all valid smaller values. Important rule: adding or subtracting the same number does not reverse the sign; multiplying or dividing by a negative number does. Exam cue: keep the inequality sign unchanged when shifting terms by addition or subtraction.