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<h1 align="center">Algebra - Substitution</h1>
<p align="center"><i>&quot;Substitute&quot; means to put in the place of another.</i></p>
<h2>Substitution</h2>
<p>In Algebra &quot;Substitution&quot; means putting numbers where the letters are:</p>
<div class="simple">
<table border="0" align="center">
<tr valign="middle">
<td><img src="../images/style/right-arrow.gif" width="46" height="46" alt="right arrow" /></td>
<td>When we have:</td>
<td>
<table border="0" width="150">
<tr valign="middle" bgcolor="#FFFFFF">
<td align="center" width="50" class="huge"> <b>x</b></td>
<td align="center" width="50" class="huge"> <b>&minus;</b></td>
<td align="center" width="50" class="huge"> <b>2</b></td>
</tr>
</table> </td>
</tr>
<tr valign="middle">
<td><img src="../images/style/right-arrow.gif" width="46" height="46" alt="right arrow" /></td>
<td>And we know that <b>x=6</b> ...</td>
<td>&nbsp;</td>
</tr>
<tr valign="middle">
<td><img src="../images/style/right-arrow.gif" width="46" height="46" alt="right arrow" /></td>
<td> ... then we can &quot;substitute&quot; <b>6</b> for <b>x</b>:</td>
<td>
<table border="0" align="left" width="250">
<tr valign="middle" bgcolor="#FFFFFF">
<td align="center" width="50" class="huge"> <b style="color:blue;">6</b></td>
<td align="center" width="50" class="huge"><b>&minus;</b></td>
<td align="center" width="50" class="huge"> <b>2</b></td>
<td align="center" width="50" class="huge"> <b>=</b></td>
<td align="center" width="50" class="huge"> <b>4</b></td>
</tr>
</table> </td>
</tr>
</table>
</div>
<p>&nbsp;</p>
<div class="example">
<h3>Example: When x=2, what is <b>10/x + 4</b> ?<br />
</h3>
<p>Put &quot;2&quot; where &quot;x&quot; is: </p>
<p align="center" class="large">10/<span class="hilite">2</span> + 4 = 5 + 4 = <b>9</b></p>
</div><div class="example">
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/substitution.gif" width="185" height="139" alt="substitute x=5 into x+x/2 becomes 5+5/2 " /><br />
<h3 class="larger">Example: When x=5, what is <b>x + x/2</b> ?</h3>
</p>
<p>Put &quot;5&quot; where &quot;x&quot; is: </p>
<p align="center" class="large"><span class="hilite">5</span> + <span class="hilite">5</span>/2 = 5 + 2.5 = <b>7.5</b></p>
</div>
<div class="example">
<h3>Example: If x=3 and y=4, then what is <b>x<sup>2</sup> + xy</b> ?<br />
</h3>
<p>Put &quot;3&quot; where &quot;x&quot; is, and &quot;4&quot; where &quot;y&quot; is: </p>
<p align="center" class="large"><span class="hilite">3</span><sup>2</sup> + <span class="hilite">3</span>&times;<span class="hilite">4</span> = 3&times;3 + 12 = <b>21</b></p>
</div>
<div class="example">
<h3>Example: If x=3 (but we don't know &quot;y&quot;), then what is <b>x<sup>2</sup> + xy</b> ?<br />
</h3>
<p>Put &quot;3&quot; where &quot;x&quot; is: </p>
<p align="center" class="large"><span class="hilite">3</span><sup>2</sup> + <span class="hilite">3</span>y = <b>9 + 3y</b></p>
<p align="center">(that is as far as we can get)</p>
</div>
<div class="indent50px"></div>
<p>As that last example showed, we may not always get a number for an answer, sometimes just a simpler formula.</p>
<h2>Negative Numbers</h2>
<p>When substituting negative numbers, put () around them so you get the calculations right.</p>
<div class="example">
<h3>Example: If x = <b>&minus;2</b>, then what is <b>1 &minus; x + x<sup>2</sup></b> ?<br />
</h3>
<p>Put &quot;(&minus;2)&quot; where &quot;x&quot; is:</p>
<p align="center" class="large"><span class="larger"><b>1 &minus; </b></span><span class="hilite"><b>(&minus;2)</b></span><span class="larger"><b> + </b></span><span class="hilite"><b>(&minus;2)</b></span><span class="larger"><b><sup>2</sup></b></span> <span class="large">= 1 + 2 + 4 = 7</span>
</p>
</div>
<p>&nbsp;</p>
<p>In that last example:</p>
<ul>
<li>the <b>&minus; (&minus;2)</b> became <b>+2</b></li>
<li>the <b>(&minus;2)<sup>2</sup></b> became <b>+4</b></li>
</ul>
<p>because of these special rules:</p>
<table border="0" align="center" cellpadding="3">
<tr>
<td>&nbsp;</td>
<th>Rule</th>
<th align="center"><a href="../positive-negative-integers.html">Adding or <br />
Subtracting</a></th>
<th width="20" align="center">&nbsp;</th>
<th align="center"><a href="../multiplying-negatives.html">Multiplying or <br />
Dividing</a></th>
</tr>
<tr>
<td rowspan="2"><img src="../images/style/plus.gif" alt="plus" width="43" height="44" /></td>
<td rowspan="2">Two like signs become a <b>positive sign</b></td>
<td align="center">3+(+2) = 3<b> + </b>2 = 5</td>
<td align="center">&nbsp;</td>
<td align="center">3 &times; 2 = 6</td>
</tr>
<tr>
<td align="center">6&minus;(&minus;3) = 6<b> + </b>3 = 9</td>
<td align="center">&nbsp;</td>
<td align="center">(&minus;3) &times; (&minus;2) = 6</td>
</tr>
<tr>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td align="center">&nbsp;</td>
<td align="center">&nbsp;</td>
<td align="center">&nbsp;</td>
</tr>
<tr>
<td rowspan="2"><img src="../images/style/minus.gif" alt="minus" width="44" height="44" /></td>
<td rowspan="2">Two unlike signs become a <b>negative sign</b> &nbsp;</td>
<td align="center">7+(&minus;2) = 7 <b>&minus; </b>2 = 5</td>
<td align="center">&nbsp;</td>
<td align="center">3 &times; (&minus;2) = &minus;6</td>
</tr>
<tr>
<td align="center">8&minus;(+2) = 8 <b>&minus; </b>2 = 6</td>
<td align="center">&nbsp;</td>
<td align="center">(&minus;3) &times; 2 = &minus;6</td>
</tr>
</table>
<p>&nbsp;</p>
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