<p><span style="font-size:22px"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-solving-1-variable-linear-equations" target="_blank">Solving 1-Variable Linear Equations Exercise</a></span></p><p><span style="color:#27ae60;">Solving a Linear Equation</span> means to find the value of the variable (or variables) that make the equation true. To accomplish such a feat, we are often "isolating" the variable. Note the example below:</p>
<p>$$8x+13x = 42$$</p>
<p>Notice how the $x$ variable is not isolated. It's not by itself. We have to apply our equation rules in order to get that dang $x$ by itself.</p>
<ul>
<li><strong>Step 1: </strong>Combine like terms.
<ul>
<li>$21x=42$</li>
</ul>
</li>
<li><strong>Step 2</strong>: Divide both sides by $21$.
<ul>
<li>$x=2$</li>
</ul>
</li>
</ul>
<p>We did it! Notice how $x$ is now by itself. We can confidently say that $x=2$. </p>
<p><strong>NOTE: </strong>Some equations are NOT solvable or have infinite solutions. Take for example $x+y=10$. There are an infinite number of $(x,y)$ pairs that make that equation true.</p>