{"id":220769,"date":"2025-05-28T18:38:04","date_gmt":"2025-05-28T18:38:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=220769"},"modified":"2025-05-28T18:38:07","modified_gmt":"2025-05-28T18:38:07","slug":"which-expression-is-equivalent-to-the-given-expression-5","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/28\/which-expression-is-equivalent-to-the-given-expression-5\/","title":{"rendered":"Which expression is equivalent to the given expression"},"content":{"rendered":"\n

Which expression is equivalent to the given expression? 6 (2i \u2013 3) i=-3<\/p>\n\n\n\n

YOUR ANSWER CORRECT ANSWER<\/p>\n\n\n\n

5 (2i \u2013 3) i=-2
5 9+ (2\u20133) i=-2
9+ (2i \u2013 3) i=-2
5
5 -9+ (2i \u2013 3) ) i=-3<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s break down the question:<\/p>\n\n\n\n

The original expression is: \u2211i=\u221236(2i\u22123)\\sum_{i=-3}^{6}(2i – 3)<\/p>\n\n\n\n

Goal:<\/h3>\n\n\n\n

Find another expression that evaluates to the same total.<\/p>\n\n\n\n

\n\n\n\n

Step-by-step analysis:<\/h3>\n\n\n\n

We’ll compute the original summation: \u2211i=\u221236(2i\u22123)\\sum_{i=-3}^{6}(2i – 3)<\/p>\n\n\n\n

This means evaluating 2i\u221232i – 3 for each integer ii from \u22123-3 to 66:<\/p>\n\n\n\n

    \n
  • For i=\u22123i = -3: 2(\u22123)\u22123=\u22126\u22123=\u221292(-3) – 3 = -6 – 3 = -9<\/li>\n\n\n\n
  • For i=\u22122i = -2: 2(\u22122)\u22123=\u22124\u22123=\u221272(-2) – 3 = -4 – 3 = -7<\/li>\n\n\n\n
  • For i=\u22121i = -1: \u22125-5<\/li>\n\n\n\n
  • For i=0i = 0: \u22123-3<\/li>\n\n\n\n
  • For i=1i = 1: \u22121-1<\/li>\n\n\n\n
  • For i=2i = 2: 11<\/li>\n\n\n\n
  • For i=3i = 3: 33<\/li>\n\n\n\n
  • For i=4i = 4: 55<\/li>\n\n\n\n
  • For i=5i = 5: 77<\/li>\n\n\n\n
  • For i=6i = 6: 99<\/li>\n<\/ul>\n\n\n\n

    Now sum them all: \u22129\u22127\u22125\u22123\u22121+1+3+5+7+9=0-9 -7 -5 -3 -1 +1 +3 +5 +7 +9 = 0<\/p>\n\n\n\n

    So, the full expression sums to 0<\/strong>.<\/p>\n\n\n\n

    \n\n\n\n

    Analyze the answer choices:<\/h3>\n\n\n\n

    1. \u2211i=\u221225(2i\u22123)\\sum_{i=-2}^{5}(2i – 3)<\/h4>\n\n\n\n

    This excludes<\/strong> i=\u22123i = -3 and i=6i = 6<\/p>\n\n\n\n

    We saw above:<\/p>\n\n\n\n

      \n
    • i=\u22123\u21d2\u22129i = -3 \\Rightarrow -9<\/li>\n\n\n\n
    • i=6\u21d29i = 6 \\Rightarrow 9<\/li>\n<\/ul>\n\n\n\n

      So this sum omits \u22129-9 and 99, which cancel out, meaning the partial sum is also 0<\/strong>.
      \u2705 This is equivalent.<\/p>\n\n\n\n

      2. 9+\u2211i=\u221225(2i\u22123)9 + \\sum_{i=-2}^{5}(2i – 3)<\/h4>\n\n\n\n

      We just established that the summation from i=\u22122i = -2 to 55 is 0<\/strong>, so this equals 9<\/strong>.
      \u274c Not equivalent.<\/p>\n\n\n\n

      3. 9+\u2211i=\u221226(2i\u22123)9 + \\sum_{i=-2}^{6}(2i – 3)<\/h4>\n\n\n\n

      This is the same as:<\/p>\n\n\n\n

        \n
      • i=\u22122i = -2 to 66 is the original range without<\/strong> i=\u22123i = -3<\/li>\n\n\n\n
      • So total is the original sum minus<\/strong> -9**, then add 9 \u2192 net effect is cancelling out \\(-9<\/li>\n\n\n\n
      • So it equals original sum: 0<\/strong>
        \u2705 This is equivalent.<\/li>\n<\/ul>\n\n\n\n

        4. \u22129+\u2211i=\u221235(2i\u22123)-9 + \\sum_{i=-3}^{5}(2i – 3)<\/h4>\n\n\n\n

        Here, i=\u22123i = -3 to 55, so it omits i=6i = 6 (which is 9), then subtracts 9.
        So it has:<\/p>\n\n\n\n

          \n
        • All terms except 9 from i=6i = 6, and subtracts 9 \u2192 net is -9 + (original sum – 9) = -18<\/strong>
          \u274c Not equivalent.<\/li>\n<\/ul>\n\n\n\n
          \n\n\n\n

          Final Answer:<\/h3>\n\n\n\n

          Both options 1 and 3 are equivalent, but the correct answer<\/strong> marked is option 1<\/strong>, which is: \u2211i=\u221225(2i\u22123)\\sum_{i=-2}^{5}(2i – 3)<\/p>\n\n\n\n

          \u2705 Correct<\/strong><\/p>\n\n\n\n

          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

          Which expression is equivalent to the given expression? 6 (2i \u2013 3) i=-3 YOUR ANSWER CORRECT ANSWER 5 (2i \u2013 3) i=-25 9+ (2\u20133) i=-29+ (2i \u2013 3) i=-255 -9+ (2i \u2013 3) ) i=-3 The Correct Answer and Explanation is: Let’s break down the question: The original expression is: \u2211i=\u221236(2i\u22123)\\sum_{i=-3}^{6}(2i – 3) Goal: Find […]<\/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-220769","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220769","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=220769"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220769\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=220769"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=220769"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=220769"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}