This question has two parts. First, answer Par Part A Solve the compound inequality 3n-4lt 4n+1leqslant A) nvert 2leqslant nlt 4 B) nvert 1lt nleqslant 5 C) nvert -5lt nleqslant 1 D) nvert -5leqslant nlt 5

To solve the compound inequality $3n-4\lt 4n+1\leqslant 5$, we need to solve each inequality separately and then combine the solutions.<br /><br />First, let's solve the inequality $3n-4\lt 4n+1$:<br />$3n-4\lt 4n+1$<br />$-n\lt 5$<br />$n\gt -5$<br /><br />Next, let's solve the inequality $4n+1\leqslant 5$:<br />$4n+1\leqslant 5$<br />$4n\leqslant 4$<br />$n\leqslant 1$<br /><br />Combining the solutions, we have $-5\lt n\leqslant 1$.<br /><br />Therefore, the correct answer is C) $\{ n\vert -5\lt n\leqslant 1\} $.