<h2>Translating to An Equation and Solving</h2>
<p>To solve applications algebraically, we will begin by translating from English sentences into equations. Our first step is to look for the word (or words) that would translate to the <strong>equals sign</strong>. The table below shows us some of the words that are commonly used.</p>
<table summary="This table has one column of eight cells. The top cell, which is a header cell, contains the word “Equals” and the equals sign. From top to bottom, the remaining seven cells read as follows: “is”, “is equal to”, “is the same as”, “the result is”, “gives”, “was”, and “will be”.">
<thead>
<tr>
<th data-valign="top"><strong>Equals =</strong></th>
</tr>
</thead>
<tbody>
<tr>
<td data-valign="top">is<br/>
is equal to<br/>
is the same as<br/>
the result is<br/>
gives<br/>
was<br/>
will be</td>
</tr>
</tbody>
</table>
<p>The steps we use to translate a sentence into an equation are listed below.</p>
<div class="ns-school-defn2">
<header>
<div data-type="title">Translate an English sentence to an algebraic equation.</div>
</header>
<ol type="1">
<li>Locate the “equals” word(s). Translate to an equals sign (=).</li>
<li>Translate the words to the left of the “equals” word(s) into an algebraic expression.</li>
<li>Translate the words to the right of the “equals” word(s) into an algebraic expression.</li>
</ol>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Translate and solve: Eleven more than <em>x</em> is equal to 54.</p>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary="This figure has two columns. At the top of the image in the left column is the word “Translate.” In the right column we have the sentence “Eleven more than x is equal to 54.” Beneath the phrase “Eleven more than x” is a curly bracket terminating in the expression x plus 11, beneath the phrase “is equal to” is a curly bracket terminating in an equal sign, and beneath the number 54 is a curly bracket terminating in 54, forming the equation: x plus 11 equals 54. One row down, the text in the left column says “Subtract 11 from both sides.” On the right is the equation with 11 subtracted from both sides: x plus 11 minus 11 equals 54 minus 11. One row down, the text in the left column says “Simplify.” In the right column is x equals 43. One row down, the columns merge into one. The text says “Check: Is 54 eleven more than 43?” Below this is the equation 43 plus 11 might equal 54. Below this is 54 equals 54 with a check mark next to it.">
<tbody>
<tr>
<td>Translate.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/6f3532fc-f5c6-44e9-9b9d-faa3fbe2735c"/></td>
</tr>
<tr>
<td>Subtract 11 from both sides.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/795aa4d2-5978-4ae4-af17-714769745c66"/></td>
</tr>
<tr>
<td>Simplify.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/dc745518-e89a-4476-88f2-1f9571587cca"/></td>
</tr>
<tr>
<td>Check: Is 54 eleven more than 43?<br/>
\(\begin{array}{ccc}\hfill 43+11&amp; \stackrel{?}{=}\hfill &amp; 54\hfill \\ \hfill 54&amp; =\hfill &amp; 54✓\hfill \end{array}\)</td>
<td> </td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Translate and solve: The difference of \(12t\) and \(11t\) is \(-14\).</p>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary="This figure has two columns. At the top of the image in the left column is the word “Translate.” In the right column we have the sentence “The difference of 12 t and 11t is negative 14.” Beneath the phrase “The difference of 12t and 11 t” is a curly bracket terminating in the expression 12 t minus 11 t, beneath the word “is” is a curly bracket terminating in an equal sign, and beneath the number negative 14 is a curly bracket terminating in negative 14, forming the equation: 12t minus 11 t equals negative 14. One row down, the text in the left column says “Simplify.” On the right is t equals negative 14. One row down, the columns merge into one. The text says “Check.” Below this is the equation 12 times negative 14 minus 11 times negative 14 might equal negative 14. Below this is negative 168 plus 154 might equal negative 14. Below this is negative 14 equals negative 14, with a check mark next to it.">
<tbody>
<tr>
<td>Translate.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/76fd30df-01f2-4af4-a03e-bbf493bff711"/></td>
</tr>
<tr>
<td>Simplify.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/b4f728ef-7f94-4845-bf35-a4c37ce9af7d"/></td>
</tr>
<tr>
<td>Check:<br/>
\(\begin{array}{ccc}\hfill 12\left(-14\right)-11\left(-14\right)&amp; \stackrel{?}{=}\hfill &amp; -14\hfill \\ \hfill -168+154&amp; \stackrel{?}{=}\hfill &amp; -14\hfill \\ \hfill -14&amp; =\hfill &amp; -14✓\hfill \end{array}\)</td>
<td> </td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>

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Translating to An Equation and Solving

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Explore different ways to solve linear equations, including using addition/subtraction and multiplication/division properties of equality and inequalities, simplifying, translating and solving word problems, and graphing inequalities on a number line.


Translating to An Equation and Solving

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