This question has two parts. First, answer Part A. Then, answer Part B. Part A Solve the compound inequality -11-2qgeqslant -21or4q+1gt 29 A) qvert qleqslant 7orqgt 9 B) qvert qleqslant 5orqgt 7 C) qvert qlt 5orqgeqslant 7 D) qvert 5leqslant qlt 9

To solve the compound inequality $-11-2q\geqslant -21or4q+1\gt 29$, we need to solve each inequality separately and then combine the solutions.<br /><br />For the first inequality, $-11-2q\geqslant -21$, we can add 11 to both sides to isolate the variable term:<br />$-2q\geqslant -10$<br /><br />Next, we divide both sides by -2 to solve for q:<br />$q\leqslant 5$<br /><br />For the second inequality, $4q+1\gt 29$, we can subtract 1 from both sides to isolate the variable term:<br />$4q\gt 28$<br /><br />Then, we divide both sides by 4 to solve for q:<br />$q\gt 7$<br /><br />Combining the solutions, we have:<br />$\{ q\vert q\leqslant 5orq\gt 7\}$<br /><br />Therefore, the correct answer is B) $\{ q\vert q\leqslant 5orq\gt 7\}$.<br /><br />Part B<br />Solve the compound inequality $-11-2q\geqslant -21or4q+1\gt 29$.<br /><br />To solve the compound inequality $-11-2q\geqslant -21or4q+1\gt 29$, we need to solve each inequality separately and then combine the solutions.<br /><br />For the first inequality, $-11-2q\geqslant -21$, we can add 11 to both sides to isolate the variable term:<br />$-2q\geqslant -10$<br /><br />Next, we divide both sides by -2 to solve for q:<br />$q\leqslant 5$<br /><br />For the second inequality, $4q+1\gt 29$, we can subtract 1 from both sides to isolate the variable term:<br />$4q\gt 28$<br /><br />Then, we divide both sides by 4 to solve for q:<br />$q\gt 7$<br /><br />Combining the solutions, we have:<br />$\{ q\vert q\leqslant 5orq\gt 7\}$<br /><br />Therefore, the correct answer is B) $\{ q\vert q\leqslant 5orq\gt 7\}$.