Solve and graph the inequality. vert x+2vert geqslant 7 Choose the correct answer below. A. xgeqslant 5 B. -9leqslant xleqslant 5 C. xleqslant -9 or xgeqslant 5 D. xleqslant -7 or xgeqslant 7

To solve the inequality $\vert x+2\vert \geqslant 7$, we need to consider two cases:<br /><br />Case 1: $x+2 \geqslant 7$<br />In this case, we can subtract 2 from both sides of the inequality to isolate $x$:<br />$x \geqslant 5$<br /><br />Case 2: $x+2 \leqslant -7$<br />In this case, we can subtract 2 from both sides of the inequality to isolate $x$:<br />$x \leqslant -9$<br /><br />Therefore, the solution to the inequality is $x \leqslant -9$ or $x \geqslant 5$.<br /><br />The correct answer is C. $x\leqslant -9$ or $x\geqslant 5$.