{"id":5327,"date":"2022-02-06T17:50:41","date_gmt":"2022-02-06T17:50:41","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=5327"},"modified":"2022-02-06T17:51:07","modified_gmt":"2022-02-06T17:51:07","slug":"solving-multi-step-equations","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/solving-multi-step-equations\/","title":{"rendered":"Solving Multi-Step Equations"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Solving Multi-Step Equations<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The term \u201cmulti\u201d means many or more than two. Therefore, a multi-step equation can be defined as an algebraic expression that requires several operations such as addition, subtraction, division, and exponentiation to be solved. Multi-step equations are solved by applying similar techniques used in solving one-step and two-step equations.<\/p>\n<p>Like we saw in one-step and two-step equations, the main objective of solving multi-step equations is to isolate the unknown variable on either the RHS or LHS of the equation while keeping a constant term on the opposite side. The strategy of obtaining a variable with a coefficient of one entails several processes.<\/p>\n<p>The Law of equations is the most important rule you should remember while solving any linear equation. This implies that, whatever you do to one side of the equation, you MUST do to the opposite of the equation.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]1. Eliminate any grouping symbols such as parentheses, braces, and brackets by employing the distributive property of multiplication over addition.<br \/>\n2. Simplify both sides of the equation by combining like terms.<br \/>\n3 Isolate a variable on any side of the equation depending on your preference.<br \/>\n4. A variable is isolated, performing the two opposite operations, such as addition and subtraction followed by multiplication and division.[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">Solve for k.<\/span><\/strong><br \/>\n<strong>3(k – 2) + k = 5(k + 3) – 9<\/strong><br \/>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]3(k – 2) + k = 5(k + 3) – 9<\/p>\n<p>3k – 6 + k = 5k + 15 – 9<\/p>\n<p>4k – 6 = 5k + 6<\/p>\n<p>4k – 5k = 6 + 6<\/p>\n<p><span style=\"color: red;\"> <strong>-k = 12<\/strong><\/span> or <span style=\"color: red;\"> <strong>k = -12<\/strong><\/span><br \/>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Solving Multi-Step Equations[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">Solve for c. <\/span><\/strong><br \/>\n7(c – 5) – 3c = 4(2c + 3) – 11<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-multi-step-equations\"><img loading=\"lazy\" class=\"alignnone wp-image-5329 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/5-22.png\" alt=\"\" width=\"104\" height=\"38\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-multi-step-equations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">Solve for d. If necessary, round to the nearest tenth. <\/span><\/strong><br \/>\n2.1(d + 7) – 30.5d = -21(d – 1) + 12.2<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-multi-step-equations\"><img loading=\"lazy\" class=\"alignnone wp-image-5331 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/6-26.png\" alt=\"\" width=\"100\" height=\"36\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-multi-step-equations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">Aiden found a big bag of table tennis balls in a clearance bin at a sports store. When she opens the bag to see how many tennis balls are in the bag, the bag breaks, sending the balls in several directions. Two-thirds of the balls rolled onto the floor, one-sixth landed in her lap, one-twelfth rolled under her bed and 3 were still in the bag. How many tennis balls were in the unopened bag?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-multi-step-equations\"><img loading=\"lazy\" class=\"alignnone wp-image-5333 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/7-24.png\" alt=\"\" width=\"192\" height=\"34\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-multi-step-equations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]<strong>Variable:<\/strong> A symbol, usually a letter, used to represent a number in mathematical expressions or sentences.<\/p>\n<p><strong>Equation:<\/strong> A mathematical sentence stating that two quantities are equal.<\/p>\n<p><strong>One-Step Equation:<\/strong> An equation that contains one operation.<\/p>\n<p>A <strong>two-step equation<\/strong> is an algebraic equation that takes you two steps to solve.<\/p>\n<p><strong>Multi-step equations<\/strong> are algebraic expressions that require more than one operation, such as subtraction, addition, multiplication, division, or exponentiation, to solve.<\/p>\n<p><strong>Distributive Property<\/strong> \u2013 to multiply a sum or difference by a number, multiply each term inside the parentheses by the number outside the parentheses.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-one-step-equations-by-addition-and-subtraction\"><span style=\"color: #ed5600;\">Solve One-Step Equations by Addition and Subtraction<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-one-step-equations-by-multiplying-and-dividing\"><span style=\"color: #ed5600;\">Solve One-Step Equations by Multiplying and Dividing<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-equations-with-rational-coefficients\"><span style=\"color: #ed5600;\">Solve Equations with Rational Coefficients<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-two-step-equations\"><span style=\"color: #ed5600;\">Solve Two-Step Equations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/Solve%20Two-Sided%20Equations%20with%20Rational%20Coefficients\"><span style=\"color: #ed5600;\">Solve Two-Sided Equations with Rational Coefficients<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/write-two-step-equations\"><span style=\"color: #ed5600;\">Write Two-Step Equations<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1637236712562{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/direct-variation-equations-y-mx-\"><span style=\"color: #333399;\">Direct Variation Equations (y = mx)<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/slope-intercept-form-of-an-equation\"><span style=\"color: #333399;\">Slope-intercept Form of an Equation<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/graphing-lines-using-intercepts\"><span style=\"color: #333399;\">Graphing Lines Using Intercepts<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/write-linear-equations\"><span style=\"color: #333399;\">Write Linear Equations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solutions-of-systems-of-equations\"><span style=\"color: #333399;\">Solutions of Systems of Equations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-linear-systems-of-equations-by-graphing\"><span style=\"color: #333399;\">Solve Linear Systems of Equations by Graphing<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-substitution\"><span style=\"color: #333399;\">Solve Systems of Equations by Substitution<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-elimination\"><span style=\"color: #333399;\">Solve Systems of Equations by Elimination<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/applications-of-systems\"><span style=\"color: #333399;\">Applications of Systems<\/span><\/a><br \/>\n[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||”][vc_btn title=”Grade 4″ color=”blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F4th-grade%2Fmaths|title:Grade%204%20Math||”][vc_btn title=”Grade 5″ color=”green” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F5th-grade%2Fmaths|title:Grade%205%20Math||”][vc_btn title=”Grade 6″ color=”info” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F6th-grade%2Fmaths|title:Grade%206%20Math||”][vc_btn title=”Grade 7″ color=”vista-blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F7th-grade%2Fmaths|title:Grade%207%20Math||”][vc_btn title=”Grade 8″ color=”mulled-wine” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F8th-grade%2Fmaths|title:Grade%208%20Math||”][\/vc_column_inner][\/vc_row_inner][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Algebra” color=”warning” link=”url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Falgebra|title:Algebra||”][vc_btn title=”Functions and equations” color=”danger” link=”url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Ffunctions-and-equations|title:Functions%20and%20equations||”][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Solving Multi-Step Equations [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The term \u201cmulti\u201d means many or more than two. Therefore, a multi-step equation can be defined as an algebraic expression that requires several operations such as addition, subtraction, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Solving Multi-Step Equations | Oryx Learning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/oryxlearning.com\/learn\/solving-multi-step-equations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Solving Multi-Step Equations\" \/>\n<meta property=\"og:description\" content=\"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Solving Multi-Step Equations [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The term \u201cmulti\u201d means many or more than two. 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