The system of linear inequalities \(2x - 1 \ge 3\) and \(x - 3 \gt 5\) has solution:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \((8, \infty)\)
Solving each inequality:
\(2x - 1 \ge 3 \Rightarrow 2x \ge 4 \Rightarrow x \ge 2\)
\(x - 3 \gt 5 \Rightarrow x \gt 8\)
The solution of the system is the common part of the two sets. Every x > 8 also satisfies x ≥ 2, so the solution is x > 8, that is \((8, \infty)\).