<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 600px;"><colgroup><col style="width: 50.0000%;"><col style="width: 50.0000%;"></colgroup><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p><strong>Properties</strong></p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p><strong>Examples</strong></p></th></tr></thead><tbody><tr style="height: 80px;"><td style="height: 80px; min-height: 80px; text-align: center; --cell-justify: center"><p>If \(x\ge y\)and \(d&gt;0\)(positive number) , then&nbsp;&nbsp; \(dx\ge dy\) and \(\frac{x}{d}\ge \frac{y}{d}\) (sign is not reversed)</p></td><td style="height: 80px; min-height: 80px; text-align: center; --cell-justify: center"></td></tr><tr style="height: 80px;"><td style="height: 80px; min-height: 80px; text-align: center; --cell-justify: center"><p>If \(x\le y\) and \(d&gt;0\)(positive number) , then</p><p>\(dx\le dy\) and \(\frac{x}{d}\le \frac{y}{d}\) (sign is not reversed)</p></td><td style="height: 80px; min-height: 80px; text-align: center; --cell-justify: center"></td></tr><tr style="height: 80px;"><td style="height: 80px; min-height: 80px; text-align: center; --cell-justify: center"><p>If \(x\ge y\) and \(d&lt;0\), then \(dx\le dy\) and \(x/d\le y/d\).</p></td><td style="height: 80px; min-height: 80px; text-align: center; --cell-justify: center"></td></tr><tr style="height: 80px;"><td style="height: 80px; min-height: 80px; text-align: center; --cell-justify: center"><p>If \(x\le y\) and \(d&lt;0\), then \(dx\ge dy\) and \(x/d\ge y/d\).</p></td><td style="height: 80px; min-height: 80px; text-align: center; --cell-justify: center"></td></tr></tbody></table></div></div>
<p>Inequality sign <strong>does not change</strong> when we multiply or divide by a <strong>positive number</strong> on both sides of inequality but </p>
<p>Inequality sign <strong>changes</strong> when when we multiply or divide by a <strong>negative number</strong> on both sides of inequality.</p>

Inequality sign **does not change** when we multiply or divide by a **positive number** on both sides of inequality but 

Inequality sign **changes** when when we multiply or divide by a **negative number** on both sides of inequality.

Properties	Examples
If \(x\ge y\)and \(d>0\)(positive number) , then \(dx\ge dy\) and \(\frac{x}{d}\ge \frac{y}{d}\) (sign is not reversed)
If \(x\le y\) and \(d>0\)(positive number) , then \(dx\le dy\) and \(\frac{x}{d}\le \frac{y}{d}\) (sign is not reversed)
If \(x\ge y\) and \(d<0\), then \(dx\le dy\) and \(x/d\le y/d\).
If \(x\le y\) and \(d<0\), then \(dx\ge dy\) and \(x/d\ge y/d\).

Solving Inequalities by Multiplication or Division

Solving Inequalities by Multiplication or Division

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