<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-inequalities-iii" target="_blank">Inequalities III Exercise</a></p>
<p><strong>Note</strong>: in the last example covered in the video, Greg uses a closed circle to indicate the starting/ending points where the inequality is valid. The problem is that the inequality is strict and not slack (i.e, > not ≥) so he was <em>technically</em> supposed to use an <strong>open</strong> circle (i.e, ○ and not ⚫) as a result, which he indeed did when covering the topic on Inequalities I two videos back. The reason we italise this is that we could not find any mention of this on the GRE Math Review or the GRE Math Conventions, so it's something ETS apparently doesn't care or test students on. We still include this note for completeness though.</p><p>The last thing to mention about inequalities in <span style="color:#27ae60;">Solving Inequalities 3</span> is that, when dealing with absolute values, <strong>two</strong> inequalities are created. For the first, just remove the absolute value sign and change nothing else. For the second, make it negative and FLIP the sign.</p>
<p><strong><span style="color:#8e44ad;">Example</span></strong></p>
<p>$$|x| > 10$$</p>
<p>results in </p>
<p>$$x > 10$$</p>
<p><strong>and</strong></p>
<p>$$x < -10$$</p>