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      <text>3.1.1.1 Introduction</text>
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      <text><![CDATA[<h3><span>Linear equations</span><br></h3>

<div class="HELM_keypoint">
<h4>Key Point</h4>
<p>A <b>linear equation</b> is an equation of the form.</p>
<p>\(ax+b=0 \qquad a\ne 0\) .</p>
<p>where \(a\) and \(b\) are known numbers and \(x\) represents an unknown quantity to be found.</p>
</div>

<p><br></p><p>In the equation \(ax+b=0\), the number \(a\) is called the <strong>coefficient of</strong> \(x\), and the number \(b\) is called the <strong>constant term</strong>.</p> <p>The following are examples of linear equations</p> 
<ul>
<li>\(3x+4=0\), </li><br>
<li>\(-2x+3=0\),  </li><br>
<li>\(-\dfrac{1}{2}x-3=0\). </li>
</ul>
<p>Note that the unknown, \(x\), appears only to the first power, that is as \(x\), and not as \(x^2\), \(\sqrt{x}\), \(x^\frac{1}{2}\) etc. Linear equations often appear in a non-standard form, and also different letters are sometimes used for the unknown quantity. For example 
</p><ul>
<li>\( 2x=x+1\), </li><br>
<li>\(3t-7=17\),</li><br>
<li>\(13=3z+1\),</li><br>
<li>\(1-\dfrac{1}{2}y=3\), </li><br>
<li>\(2\alpha-1.5=0\), </li><br>
</ul>
are all examples of linear equations. Where necessary the equations can be rearranged and written in the form \(ax+b=0\). We will explain how to do this later in this Section.

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