<p><span style="font-size:22px"><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-introduction-to-equations">Introduction to Equations Exercise</a></span></p><p>Equations are basically just algebraic expressions with an equals sign.</p>
<p>According to ETS, solving an equation means:</p>
<blockquote>
<p>Find the value(s) of the variable(s) that make(s) the equation true.</p>
</blockquote>
<p>Some equations have one solution: $x+8=10$</p>
<ul>
<li>Here, the only value for $x$ that would work is $x=2$.</li>
</ul>
<p>Sometimes there are 2 solutions:</p>
<ul>
<li>For example, with $x^2=81$, $x$ could be $\sqrt{81}$ or $-\sqrt{81}$ , which are $9$ and $-9$ respectively.</li>
<li>Another example would be $x^2+7x+12=0$. We can convert this to $(x+3)(x+4)=0$, and we know that both $x=-3$ or $x=-4$ would work here.</li>
</ul>
<p>Sometimes there can be infinite solutions.</p>
<ul>
<li>Think about something like $m+n=10$. $m$ and $n$ can be any pair of values, as long as they add up to $10$.</li>
</ul>