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\( 23 more than Gails age is 42 use the variable g to represent Gails age  \)

<h2>Translating Word Phrases to Algebraic Equations</h2>
<p>Remember, an equation has an equal sign between two algebraic expressions. So if we have a sentence that tells us that two phrases are equal, we can translate it into an equation. We look for clue words that mean <em>equals</em>. Some words that translate to the equal sign are:</p>
<ul data-bullet-style="bullet">
<li>is equal to</li>
<li>is the same as</li>
<li>is</li>
<li>gives</li>
<li>was</li>
<li>will be</li>
</ul>
<p>It may be helpful to put a box around the <em>equals</em> word(s) in the sentence to help you focus separately on each phrase. Then translate each phrase into an expression, and write them on each side of the equal sign.</p>
<p>We will practice translating word sentences into algebraic equations. Some of the sentences will be basic number facts with no variables to solve for. Some sentences will translate into equations with variables. The focus right now is just to translate the words into algebra.</p>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<p>Translate the sentence into an algebraic equation: The sum of <span tabindex="0">\(6\) and \(9\) is \(15.\)</span></p>
</div>
<div>
<h3 data-type="title">Solution</h3>
<p>The word <em>is</em> tells us the equal sign goes between 9 and 15.</p>
<table data-label="" summary="The image is 2 columns. The left column shows instructions and the right column shows word expressions and expressions. The first line in the left column says “locate the equals words”.  Next to this is “the sum of 6 and 9 is 15.” There is a box around the word is to highlight that this word represents equal to. The next line on the left says “write the equal to sign”. Now the sentence becomes “The sum of 6 and 9 equal to symbol 15.” There is an arrow pointing downward from the word is in the previous statement to the equal sign in the expression. The next line reads “translate the words to the left of the equals word into an algebraic expression”. Next to this, is the incomplete expression 6 plus 9 equals a blank line. The last line in the left column reads “translate the words to the right of the equals word into an algebraic expression.” Next to this is the full expression 6 plus 9 equals 15.">
<tbody>
<tr>
<td>Locate the “equals” word(s).</td>
<td rowspan="2"><img alt="." src="https://data.ulearngo.com/assets/1f047b68-6166-4dd1-9389-69a8a52cd47e"/></td>
</tr>
<tr>
<td>Write the = sign.</td>
<td> </td>
</tr>
<tr>
<td>Translate the words to the left of the <em>equals</em> word into an algebraic expression.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/a0b97b8b-a339-472d-89df-ea18ff519f32"/></td>
</tr>
<tr>
<td>Translate the words to the right of the <em>equals</em> word into an algebraic expression.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/f8d44787-91d1-4a62-88b6-444f251389e9"/></td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<p>Translate the sentence into an algebraic equation: The product of <span tabindex="0">\(8\) and \(7\) is \(56.\)</span></p>
</div>
<div>
<h3 data-type="title">Solution</h3>
<p>The location of the word <em>is</em> tells us that the equal sign goes between 7 and 56.</p>
<table data-label="" summary="The image shows the sentence “The product of 8 and 7 is 56.” There is a box around the word is to highlight that this word represents equal to. Now the sentence becomes “The product of 8 and 7 equal to symbol 56.” The words to the left of the equal to symbol, the product of 8 and 7 can be written as the number 8 dot multiplication symbol the number 7. The words to the right of the equal to symbol is 56. The algebraic equation is 8 times 7 equal to 56.">
<tbody>
<tr>
<td>Locate the “equals” word(s).</td>
<td rowspan="2"><img alt="." src="https://data.ulearngo.com/assets/477ae0e1-20f5-4f35-b5e5-d5ccaa2e71e1"/></td>
</tr>
<tr>
<td>Write the = sign.</td>
<td> </td>
</tr>
<tr>
<td>Translate the words to the left of the <em>equals</em> word into an algebraic expression.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/3ac79f72-5da1-4abb-b1b1-02dfb3cecc07"/></td>
</tr>
<tr>
<td>Translate the words to the right of the <em>equals</em> word into an algebraic expression.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/8491ec15-acb5-4c2b-80eb-9d09e7fe7351"/></td>
</tr>
</tbody>
</table>
</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 the sentence into an algebraic equation: Twice the difference of <span tabindex="0">\(x\) and \(3\) gives \(18.\)</span></p>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary="The image shows the sentence “Twice the difference of x and 3 gives 18.” There is a box around the word gives to highlight that this word represents equal to. Twice means 2 times. The difference of x and 3 means x minus 3. The equation becomes 2 times open parentheses x minus 3 close parentheses equal to 18.">
<tbody>
<tr>
<td>Locate the “equals” word(s).</td>
<td><img alt="." src="https://data.ulearngo.com/assets/26cfae94-af0d-4b26-b72c-033a925dc8aa"/></td>
</tr>
<tr>
<td>Recognize the key words: <em>twice; difference of …. and …</em>.</td>
<td><em>Twice</em> means two times.</td>
</tr>
<tr>
<td>Translate.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/9f13782b-88cc-4b33-af74-63b2690cf7d3"/> </td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<h2 data-type="title">Translate to an Equation and Solve</h2>
<p>Now let’s practice translating sentences into algebraic equations and then solving them. We will solve the equations by using the Subtraction and Addition Properties of Equality.</p>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<p>Translate and solve: Three more than <span tabindex="0">\(x\) is equal to \(47.\)</span></p>
</div>
<div>
<h3 data-type="title">Solution</h3>
<table data-label="" summary="From the equation x plus 3 equals 47, subtract 3 from both sides. The left side simplifies to just x. The right side is 47 minus 3 to get 44. The equation becomes x equal to 44. Check by letting x be 44 in the original equation. Is 44 plus 3 equal to 47? Yes.">
<tbody>
<tr>
<td colspan="2"> </td>
<td>Three more than <em>x</em> is equal to 47.</td>
</tr>
<tr>
<td colspan="2">Translate.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/eecf049d-80a9-4ff8-997e-b894fd40893a"/></td>
</tr>
<tr>
<td colspan="2">Subtract 3 from both sides of the equation.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/199453ff-ec01-4274-b3fb-6b82f1c62732"/></td>
</tr>
<tr>
<td colspan="2">Simplify.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/dab71363-d16d-44c2-859c-695365f30f32"/></td>
</tr>
<tr>
<td>We can check. Let \(x=44\).</td>
<td><img alt="." src="https://data.ulearngo.com/assets/25eb5287-14cb-4dee-9bff-176738eb9c9b"/></td>
<td> </td>
</tr>
<tr>
<td> </td>
<td><img alt="." src="https://data.ulearngo.com/assets/234c94fa-1b99-4c79-81ec-57b0dae89542"/></td>
<td> </td>
</tr>
<tr>
<td> </td>
<td><img alt="." src="https://data.ulearngo.com/assets/56591bbf-d25c-4a5f-86c1-bbfcda96e2b8"/></td>
<td> </td>
</tr>
</tbody>
</table>
<p>So \(x=\text{}\phantom{\rule{0.2em}{0ex}}44\) is the solution.</p>
</div>
</div>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<p>Translate and solve: The difference of <span tabindex="0">\(y\) and \(14\) is \(18.\)</span></p>
</div>
<div>
<h3 data-type="title">Solution</h3>
<table data-label="" summary="The image shows the sentence “The difference of y and 14 is 18.” Translate that to an algebraic equation to get y minus 14 equal to 18. Add 14 to both sides. The left side simplifies to y and the right is 18 plus 14 which is 32. The equation becomes y equal to 32. Substitute 32 back into the equation for y to check. Is 32 minus 14 equal to 18. Yes.">
<tbody>
<tr>
<td colspan="2"> </td>
<td>The difference of <em>y</em> and 14 is 18.</td>
</tr>
<tr>
<td colspan="2">Translate.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/16ce07cf-0b7a-45aa-a8c2-05e1e35b1a7b"/></td>
</tr>
<tr>
<td colspan="2">Add 14 to both sides.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/6963dc99-03c1-4303-b936-b1db08f992f0"/></td>
</tr>
<tr>
<td colspan="2">Simplify.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/4a93c095-35a6-462c-a954-8cda63166f0b"/></td>
</tr>
<tr>
<td>We can check. Let \(y=32\).</td>
<td><img alt="." src="https://data.ulearngo.com/assets/6fe51748-7d10-4270-bc1a-29d77d4883a8"/></td>
<td> </td>
</tr>
<tr>
<td> </td>
<td><img alt="." src="https://data.ulearngo.com/assets/3e9bd732-b071-47e7-8b2a-4cc542e0d50d"/></td>
<td> </td>
</tr>
<tr>
<td> </td>
<td><img alt="." src="https://data.ulearngo.com/assets/1cf832e9-1e0a-446e-b81d-00ccfda0ef1a"/></td>
<td> </td>
</tr>
</tbody>
</table>
<p>So \(y=32\) is the solution.</p>
</div>
</div>
</div>
</div>
<div class="media-2 ui-has-child-title" data-type="note">
<header></header>
<h2>Optional Video: Solving One Step Equations By Addition and Subtraction</h2>
<iframe allowfullscreen="allowfullscreen" frameborder="0" height="360" src="https://www.youtube.com/embed/E2povst-oYs?rel=0&amp;modestbranding=1&amp;cc_lang_pref=en&amp;cc_load_policy=1" width="640"><span class="mce_SELRES_start" data-mce-type="bookmark" style="display: inline-block; width: 0px; overflow: hidden; line-height: 0;">﻿</span></iframe></div>

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Translating Word Phrases to Algebraic Equations

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

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Learn to identify and simplify algebraic expressions, evaluate expressions, and translate word problems into algebraic equations in this comprehensive tutorial on the language of algebra.


Translating Word Phrases to Algebraic Equations

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