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

Correct answer: \(m\geq 7\)

Since \(x\geq 3\) and \(y\geq 4\), the minimum possible value of \(x+y\) occurs at \((3,4)\) and is \(3+4=7\). This point satisfies \(x+y\leq m\) only when \(m\geq 7\). For \(m=7\), the solution region consists of the single point \((3,4)\), so \(m>7\) is not necessary. Exam tip: for parameter-based inequalities, first find the minimum or maximum value of the relevant expression under the given bounds.