If the solution of ( 3x+a<12 ) is (x<2), what is the value of (a)?

Correct answer: 6

From \(3x+a<12\), we get \(3x<12-a\), so \(x<\frac{12-a}{3}\). Since the given solution is \(x<2\), the boundary values must be equal: \(\frac{12-a}{3}=2\). Thus, \(12-a=6\), giving \(a=6\). For example, if \(a=5\), the solution would be \(x<\frac{7}{3}\), not \(x<2\). Exam tip: when a solution boundary is given, equate it to the boundary expression obtained after solving the inequality.