{"id":275699,"date":"2025-07-30T02:47:16","date_gmt":"2025-07-30T02:47:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=275699"},"modified":"2025-07-30T02:47:19","modified_gmt":"2025-07-30T02:47:19","slug":"identify-equivalent-linear-expression","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/30\/identify-equivalent-linear-expression\/","title":{"rendered":"Identify equivalent linear expression"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-1177.png\" alt=\"\" class=\"wp-image-275700\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<p>Of the choices provided, all four expressions are equivalent to 6(a &#8211; 3).<\/p>\n\n\n\n<p>To determine which expressions are equivalent to 6(a &#8211; 3), we can apply fundamental properties of algebra. The original expression involves a number, 6, being multiplied by a group of terms in parentheses, (a &#8211; 3).<\/p>\n\n\n\n<p>First, we can use the distributive property. This property states that multiplying a number by a group of terms is the same as multiplying the number by each term individually. Applying this to 6(a &#8211; 3), we multiply 6 by &#8216;a&#8217; and 6 by &#8216;-3&#8217;. This gives us 6 * a &#8211; 6 * 3, which simplifies to 6a &#8211; 18. This directly confirms that the third option, 6a &#8211; 18, is equivalent.<\/p>\n\n\n\n<p>Next, we can consider the commutative property of multiplication. This rule allows us to change the order of factors in a multiplication problem without changing the result. The original expression is 6 multiplied by the quantity (a &#8211; 3). According to this property, 6 * (a &#8211; 3) is the same as (a &#8211; 3) * 6. This confirms that the fourth option, (a &#8211; 3)6, is also equivalent.<\/p>\n\n\n\n<p>We can also apply the commutative property of addition to the terms inside the parentheses. The expression &#8216;a &#8211; 3&#8217; is mathematically the same as &#8216;a + (-3)&#8217;. The commutative property of addition lets us reorder these terms to &#8216;(-3) + a&#8217;, or simply &#8216;-3 + a&#8217;. Therefore, the quantity (a &#8211; 3) is equivalent to (-3 + a). If we substitute this back into the original expression, we get 6(-3 + a), which validates the first option.<\/p>\n\n\n\n<p>Finally, by combining the commutative properties of both multiplication and addition, we can take the expression from the previous step, 6(-3 + a), and reorder the factors. This gives us (-3 + a)6, which confirms that the second option is also equivalent. All four options are mathematically identical to the original expression.<\/p>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" data-id=\"275702\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-2506.jpeg\" alt=\"\" class=\"wp-image-275702\"\/><\/figure>\n<\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Of the choices provided, all four expressions are equivalent to 6(a &#8211; 3). To determine which expressions are equivalent to 6(a &#8211; 3), we can apply fundamental properties of algebra. The original expression involves a number, 6, being multiplied by a group of terms in parentheses, (a &#8211; 3). First, we can use the distributive [&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-275699","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/275699","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=275699"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/275699\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=275699"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=275699"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=275699"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}