{"id":273750,"date":"2025-07-27T19:31:51","date_gmt":"2025-07-27T19:31:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=273750"},"modified":"2025-07-27T19:31:58","modified_gmt":"2025-07-27T19:31:58","slug":"select-the-expressions-that-are-equivalent-to-2u4-5u-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/27\/select-the-expressions-that-are-equivalent-to-2u4-5u-3\/","title":{"rendered":"Select the expressions that are equivalent to (-2u+4)+(-5u-3)"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-1003.png\" alt=\"\" class=\"wp-image-273752\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Of the choices provided, the following three expressions are equivalent to&nbsp;(-2u + 4) + (-5u &#8211; 3):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>-7u + 1<\/strong><\/li>\n\n\n\n<li><strong>-7u &#8211; 3 + 4<\/strong><\/li>\n\n\n\n<li><strong>(-5u + -3) + (-2u + 4)<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>To find the equivalent expressions, we first need to simplify the original expression,&nbsp;(-2u + 4) + (-5u &#8211; 3). The process involves combining like terms, which are terms that have the same variable raised to the same power.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Remove the Parentheses:<\/strong>\u00a0Since the two groups of terms are being added, we can remove the parentheses without changing the signs of any terms inside.<br>(-2u + 4) + (-5u &#8211; 3)\u00a0becomes\u00a0-2u + 4 &#8211; 5u &#8211; 3.<\/li>\n\n\n\n<li><strong>Group Like Terms:<\/strong>\u00a0Next, we rearrange the expression to group the variable terms (those with &#8216;u&#8217;) together and the constant terms (the numbers) together.<br>(-2u &#8211; 5u) + (4 &#8211; 3)<\/li>\n\n\n\n<li><strong>Combine Like Terms:<\/strong>\u00a0Now, we perform the calculations for each group.\n<ul class=\"wp-block-list\">\n<li>For the variable terms:\u00a0-2u &#8211; 5u = -7u<\/li>\n\n\n\n<li>For the constant terms:\u00a04 &#8211; 3 = 1<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>Combining these results gives us the fully simplified expression:&nbsp;<strong>-7u + 1<\/strong>.<\/p>\n\n\n\n<p>Now, let&#8217;s analyze each option:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>-5u = -2u + 4 &#8211; 3: This is an equation, not an expression, because of the equals sign. An equation asserts that two sides are equal, while an expression is a mathematical phrase. Therefore, it cannot be equivalent.<\/li>\n\n\n\n<li><strong>-7u + 1<\/strong>: This matches our simplified result perfectly. It is the most common and direct simplification of the original expression.<\/li>\n\n\n\n<li><strong>-7u &#8211; 3 + 4<\/strong>: This expression is equivalent because it represents a valid intermediate step in our simplification. The &#8216;u&#8217; terms (-2u\u00a0and\u00a0-5u) have been combined to get\u00a0-7u, but the constant terms (-3\u00a0and\u00a0+4) have not yet been combined. If you simplify this expression further, you get\u00a0-7u + 1.<\/li>\n\n\n\n<li><strong>(-5u + -3) + (-2u + 4)<\/strong>: This expression is equivalent due to the\u00a0<strong>Commutative Property of Addition<\/strong>, which states that the order in which you add numbers or terms does not change the sum (for example, a + b = b + a). This option simply reverses the order of the two original parenthetical groups, which results in the same final answer.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-2334.jpeg\" alt=\"\" class=\"wp-image-273753\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: Of the choices provided, the following three expressions are equivalent to&nbsp;(-2u + 4) + (-5u &#8211; 3): Explanation To find the equivalent expressions, we first need to simplify the original expression,&nbsp;(-2u + 4) + (-5u &#8211; 3). The process involves combining like terms, which are terms that have the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-273750","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/273750","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=273750"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/273750\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=273750"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=273750"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=273750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}