For the solution region of \(x+y\leq m\), \(x\geq 4\), and \(y\geq 3\) to be non-empty, what is the correct condition on (m)?

Correct answer: \(m\geq 7\)

Since \(x\geq4\) and \(y\geq3\), the minimum possible value of \(x+y\) is \(7\), attained at \((4,3)\). Therefore, \(x+y\leq m\) can be satisfied only when \(m\) is at least \(7\), i.e. \(m\geq7\). Although \(m>12\) also gives a non-empty region, it is not the required condition because \(m=7\) already gives the solution point \((4,3)\). Exam tip: For parameter-based inequalities, first find the extreme possible value of the relevant expression.