If the solution of ( ax+7<1 ) is (x>3), what is the value of (a)?

Correct answer: -2

From \(ax+7<1\), we get \(ax<-6\). For the solution to be \(x>3\), \(a\) must be negative because dividing an inequality by a negative number reverses its sign. At the boundary value \(x=3\), \(3a=-6\), so \(a=-2\). Check: \(-2x+7<1\Rightarrow -2x<-6\Rightarrow x>3\). If \(a=2\), the result is \(x<-3\), so it is not correct. Exam tip: Always reverse the inequality sign when multiplying or dividing by a negative quantity.