{"id":9363,"date":"2017-05-02T21:50:32","date_gmt":"2017-05-02T21:50:32","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9363"},"modified":"2020-01-09T00:22:32","modified_gmt":"2020-01-09T00:22:32","slug":"translating-words-into-an-algebriac-equation-and-solving","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/translating-words-into-an-algebriac-equation-and-solving\/","title":{"raw":"Translating Words Into an Algebraic Equation and Solving","rendered":"Translating Words Into an Algebraic Equation and Solving"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Translate statements into algebraic equations involving addition, subtraction, multiplication, and division<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Translate Word Phrases to Algebraic Equations<\/h2>\r\nRemember, 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:\r\n<ul id=\"fs-id2494527\">\r\n \t<li>is equal to<\/li>\r\n \t<li>is the same as<\/li>\r\n \t<li>is<\/li>\r\n \t<li>gives<\/li>\r\n \t<li>was<\/li>\r\n \t<li>will be<\/li>\r\n<\/ul>\r\nIt 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.\r\n\r\nWe 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.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate the sentence into an algebraic equation: The sum of [latex]6[\/latex] and [latex]9[\/latex] is [latex]15[\/latex].\r\n\r\nSolution\r\nThe word <em>is<\/em> tells us the equal sign goes between 9 and 15.\r\n<table id=\"eip-id1168468614513\" class=\"unnumbered unstyled\" 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 \">\r\n<tbody>\r\n<tr>\r\n<td>Locate the \"equals\" word(s).<\/td>\r\n<td rowspan=\"2\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215934\/CNX_BMath_Figure_02_03_032-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the = sign.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate the words to the left of the <em>equals<\/em> word into an algebraic expression.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215935\/CNX_BMath_Figure_02_03_032-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate the words to the right of the <em>equals<\/em> word into an algebraic expression.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215936\/CNX_BMath_Figure_02_03_032-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146545[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate the sentence into an algebraic equation: The product of [latex]8[\/latex] and [latex]7[\/latex] is [latex]56[\/latex].\r\n[reveal-answer q=\"114417\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"114417\"]\r\n\r\nSolution\r\nThe location of the word <em>is<\/em> tells us that the equal sign goes between 7 and 56.\r\n<table id=\"eip-id1168468415970\" class=\"unnumbered unstyled\" summary=\"The image shows the sentence \">\r\n<tbody>\r\n<tr>\r\n<td>Locate the \"equals\" word(s).<\/td>\r\n<td rowspan=\"2\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215937\/CNX_BMath_Figure_02_03_028_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the = sign.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate the words to the left of the <em>equals<\/em> word into an algebraic expression.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215938\/CNX_BMath_Figure_02_03_028_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate the words to the right of the <em>equals<\/em> word into an algebraic expression.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215939\/CNX_BMath_Figure_02_03_028_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146546[\/ohm_question]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate the sentence into an algebraic equation: Twice the difference of [latex]x[\/latex] and [latex]3[\/latex] gives [latex]18[\/latex].\r\n[reveal-answer q=\"79895\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"79895\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469837874\" class=\"unnumbered unstyled\" summary=\"The image shows the sentence \">\r\n<tbody>\r\n<tr>\r\n<td>Locate the \"equals\" word(s).<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215940\/CNX_BMath_Figure_02_03_029_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recognize the key words: <em>twice; difference of \u2026. and \u2026<\/em>.<\/td>\r\n<td><em>Twice<\/em> means two times.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215942\/CNX_BMath_Figure_02_03_029_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]2(x-3)=18[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146549[\/ohm_question]\r\n\r\n[ohm_question]146550[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Translate to an Equation and Solve<\/h2>\r\nNow let\u2019s practice translating sentences into algebraic equations and then solving them. We will solve the equations by using the Subtraction and Addition Properties of Equality.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate and solve: Three more than [latex]x[\/latex] is equal to [latex]47[\/latex].\r\n[reveal-answer q=\"989526\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"989526\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469829072\" class=\"unnumbered unstyled\" 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.\">\r\n<tbody>\r\n<tr>\r\n<td colspan=\"2\"><\/td>\r\n<td>Three more than <em>x<\/em> is equal to [latex]47[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Translate.<\/td>\r\n<td>[latex]x+3=47[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Subtract [latex]3[\/latex] from both sides of the equation.<\/td>\r\n<td>[latex]x+3\\color{red}{--3}=47\\color{red}{--3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Simplify.<\/td>\r\n<td>[latex]x=44[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We can check. Let [latex]x=44[\/latex] .<\/td>\r\n<td>[latex]x+3=47[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]44+3=47[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]47=47\\quad\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSo [latex]x=\\text{}44[\/latex] is the solution.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146551[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate and solve: The difference of [latex]y[\/latex] and [latex]14[\/latex] is [latex]18[\/latex].\r\n[reveal-answer q=\"763260\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"763260\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469862237\" class=\"unnumbered unstyled\" summary=\"The image shows the sentence \">\r\n<tbody>\r\n<tr>\r\n<td colspan=\"2\"><\/td>\r\n<td>The difference of [latex]y[\/latex] and [latex]14[\/latex] is [latex]18[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Translate.<\/td>\r\n<td>[latex]y-14=18[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Add [latex]14[\/latex] to both sides.<\/td>\r\n<td>[latex]y-14\\color{red}{+14}=18\\color{red}{+14}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Simplify.<\/td>\r\n<td>[latex]y=32[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We can check. Let [latex]y=32[\/latex] .<\/td>\r\n<td>[latex]y--14=18[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]32--14=18[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]18=18\\quad\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSo [latex]y=32[\/latex] is the solution.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146552[\/ohm_question]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\nIn the following video we show more examples of how to translate an equation into\u00a0words and solve. Note that this is different from the written examples on this page because we start with the mathematical equation then translate it into words.\r\n\r\nhttps:\/\/youtu.be\/tubom5d5lxg","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate statements into algebraic equations involving addition, subtraction, multiplication, and division<\/li>\n<\/ul>\n<\/div>\n<h2>Translate Word Phrases to Algebraic Equations<\/h2>\n<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>\n<ul id=\"fs-id2494527\">\n<li>is equal to<\/li>\n<li>is the same as<\/li>\n<li>is<\/li>\n<li>gives<\/li>\n<li>was<\/li>\n<li>will be<\/li>\n<\/ul>\n<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>\n<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>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate the sentence into an algebraic equation: The sum of [latex]6[\/latex] and [latex]9[\/latex] is [latex]15[\/latex].<\/p>\n<p>Solution<br \/>\nThe word <em>is<\/em> tells us the equal sign goes between 9 and 15.<\/p>\n<table id=\"eip-id1168468614513\" class=\"unnumbered unstyled\" 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\">\n<tbody>\n<tr>\n<td>Locate the &#8220;equals&#8221; word(s).<\/td>\n<td rowspan=\"2\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215934\/CNX_BMath_Figure_02_03_032-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the = sign.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Translate the words to the left of the <em>equals<\/em> word into an algebraic expression.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215935\/CNX_BMath_Figure_02_03_032-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Translate the words to the right of the <em>equals<\/em> word into an algebraic expression.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215936\/CNX_BMath_Figure_02_03_032-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146545\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146545&theme=oea&iframe_resize_id=ohm146545&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate the sentence into an algebraic equation: The product of [latex]8[\/latex] and [latex]7[\/latex] is [latex]56[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q114417\">Show Solution<\/span><\/p>\n<div id=\"q114417\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nThe location of the word <em>is<\/em> tells us that the equal sign goes between 7 and 56.<\/p>\n<table id=\"eip-id1168468415970\" class=\"unnumbered unstyled\" summary=\"The image shows the sentence\">\n<tbody>\n<tr>\n<td>Locate the &#8220;equals&#8221; word(s).<\/td>\n<td rowspan=\"2\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215937\/CNX_BMath_Figure_02_03_028_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the = sign.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Translate the words to the left of the <em>equals<\/em> word into an algebraic expression.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215938\/CNX_BMath_Figure_02_03_028_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Translate the words to the right of the <em>equals<\/em> word into an algebraic expression.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215939\/CNX_BMath_Figure_02_03_028_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146546\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146546&theme=oea&iframe_resize_id=ohm146546&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate the sentence into an algebraic equation: Twice the difference of [latex]x[\/latex] and [latex]3[\/latex] gives [latex]18[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q79895\">Show Solution<\/span><\/p>\n<div id=\"q79895\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469837874\" class=\"unnumbered unstyled\" summary=\"The image shows the sentence\">\n<tbody>\n<tr>\n<td>Locate the &#8220;equals&#8221; word(s).<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215940\/CNX_BMath_Figure_02_03_029_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Recognize the key words: <em>twice; difference of \u2026. and \u2026<\/em>.<\/td>\n<td><em>Twice<\/em> means two times.<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215942\/CNX_BMath_Figure_02_03_029_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]2(x-3)=18[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146549\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146549&theme=oea&iframe_resize_id=ohm146549&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146550\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146550&theme=oea&iframe_resize_id=ohm146550&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Translate to an Equation and Solve<\/h2>\n<p>Now let\u2019s 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>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and solve: Three more than [latex]x[\/latex] is equal to [latex]47[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q989526\">Show Solution<\/span><\/p>\n<div id=\"q989526\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469829072\" class=\"unnumbered unstyled\" 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.\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td>Three more than <em>x<\/em> is equal to [latex]47[\/latex].<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Translate.<\/td>\n<td>[latex]x+3=47[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Subtract [latex]3[\/latex] from both sides of the equation.<\/td>\n<td>[latex]x+3\\color{red}{--3}=47\\color{red}{--3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td>[latex]x=44[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We can check. Let [latex]x=44[\/latex] .<\/td>\n<td>[latex]x+3=47[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]44+3=47[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]47=47\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>So [latex]x=\\text{}44[\/latex] is the solution.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146551\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146551&theme=oea&iframe_resize_id=ohm146551&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and solve: The difference of [latex]y[\/latex] and [latex]14[\/latex] is [latex]18[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q763260\">Show Solution<\/span><\/p>\n<div id=\"q763260\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469862237\" class=\"unnumbered unstyled\" summary=\"The image shows the sentence\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td>The difference of [latex]y[\/latex] and [latex]14[\/latex] is [latex]18[\/latex].<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Translate.<\/td>\n<td>[latex]y-14=18[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Add [latex]14[\/latex] to both sides.<\/td>\n<td>[latex]y-14\\color{red}{+14}=18\\color{red}{+14}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td>[latex]y=32[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We can check. Let [latex]y=32[\/latex] .<\/td>\n<td>[latex]y--14=18[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]32--14=18[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]18=18\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>So [latex]y=32[\/latex] is the solution.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146552\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146552&theme=oea&iframe_resize_id=ohm146552&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<p>In the following video we show more examples of how to translate an equation into\u00a0words and solve. Note that this is different from the written examples on this page because we start with the mathematical equation then translate it into words.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Solving Equations Using the Story of x (Part 1)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/tubom5d5lxg?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-9363\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146552, 146551, 146550. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: MathAS Community License<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Solving Equations Using the Story of x (Part 1). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/tubom5d5lxg\">https:\/\/youtu.be\/tubom5d5lxg<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Solving Equations Using the Story of x (Part 1)\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/tubom5d5lxg\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID 146552, 146551, 146550\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"MathAS Community License\"}]","CANDELA_OUTCOMES_GUID":"f58f6912-2bb6-4d65-86c7-a294ef6a636a","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9363","chapter","type-chapter","status-publish","hentry"],"part":16105,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9363","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":18,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9363\/revisions"}],"predecessor-version":[{"id":16115,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9363\/revisions\/16115"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/parts\/16105"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9363\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/media?parent=9363"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=9363"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/contributor?post=9363"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/license?post=9363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}