{"id":25192,"date":"2025-06-18T21:25:27","date_gmt":"2025-06-18T21:25:27","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25192"},"modified":"2025-06-18T21:25:29","modified_gmt":"2025-06-18T21:25:29","slug":"twice-a-number-decreased-by-8-is-2-less-than-half-the-number","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/twice-a-number-decreased-by-8-is-2-less-than-half-the-number\/","title":{"rendered":"Twice a number decreased by 8 is 2 less than half the number"},"content":{"rendered":"\n

Twice a number decreased by 8 is 2 less than half the number. What is the number?<\/p>\n\n\n\n

The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n

Let\u2019s break down the problem step by step and solve it.<\/p>\n\n\n\n

Problem:<\/h3>\n\n\n\n

\u201cTwice a number decreased by 8 is 2 less than half the number.<\/strong>\u201d<\/p>\n\n\n\n

\n\n\n\n

Step 1: Let the unknown number be xx.<\/h3>\n\n\n\n
\n\n\n\n

Step 2: Translate the sentence into an equation.<\/h3>\n\n\n\n
    \n
  • “Twice a number<\/strong>” means 2x2x<\/li>\n\n\n\n
  • “Decreased by 8<\/strong>” means 2x\u221282x – 8<\/li>\n\n\n\n
  • “Is<\/strong>” means equals (==)<\/li>\n\n\n\n
  • “2 less than half the number<\/strong>” means 12x\u22122\\frac{1}{2}x – 2<\/li>\n<\/ul>\n\n\n\n

    So, the full equation becomes: 2x\u22128=12x\u221222x – 8 = \\frac{1}{2}x – 2<\/p>\n\n\n\n

    \n\n\n\n

    Step 3: Solve the equation.<\/h3>\n\n\n\n

    Start by eliminating the fraction. Multiply every term by 2 to clear the denominator: 2(2x\u22128)=2(12x\u22122)2(2x – 8) = 2\\left(\\frac{1}{2}x – 2\\right) 4x\u221216=x\u221244x – 16 = x – 4<\/p>\n\n\n\n

    Now, solve for xx:<\/p>\n\n\n\n

    Subtract xx from both sides: 3x\u221216=\u221243x – 16 = -4<\/p>\n\n\n\n

    Add 16 to both sides: 3x=123x = 12<\/p>\n\n\n\n

    Divide both sides by 3: x=4x = 4<\/p>\n\n\n\n

    \n\n\n\n

    Step 4: Check the answer.<\/h3>\n\n\n\n
      \n
    • Twice the number: 2\u00d74=82 \\times 4 = 8<\/li>\n\n\n\n
    • Decreased by 8: 8\u22128=08 – 8 = 0<\/li>\n\n\n\n
    • Half the number: 12\u00d74=2\\frac{1}{2} \\times 4 = 2<\/li>\n\n\n\n
    • 2 less than that: 2\u22122=02 – 2 = 0<\/li>\n<\/ul>\n\n\n\n

      Both sides are equal. \u2705<\/p>\n\n\n\n

      \n\n\n\n

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

      4\\boxed{4}<\/p>\n\n\n\n

      \n\n\n\n

      Explanation (300 words):<\/h3>\n\n\n\n

      This problem is a classic example of translating a verbal statement into an algebraic equation and then solving it. The key to solving such problems lies in carefully interpreting the language.<\/p>\n\n\n\n

      The phrase “twice a number” suggests multiplication by 2, while “decreased by 8” indicates subtraction. On the other side of the equation, “2 less than half the number” reverses the usual order: it means you take half the number and then subtract 2<\/strong> \u2014 not the other way around.<\/p>\n\n\n\n

      Once the equation is formed, eliminating fractions early simplifies the process. We multiply through by 2 to make all terms easier to work with. From there, basic algebra (subtracting like terms, isolating the variable) leads us to the correct solution.<\/p>\n\n\n\n

      Verifying your answer is always a smart step. Plugging your solution back into the original sentence ensures that you interpreted the words correctly and didn\u2019t make a calculation error.<\/p>\n\n\n\n

      This approach\u2014define the variable, translate the sentence, solve the equation, and verify\u2014is reliable and can be applied to a wide range of word problems in algebra.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Twice a number decreased by 8 is 2 less than half the number. What is the number? The correct answer and explanation is: Let\u2019s break down the problem step by step and solve it. Problem: \u201cTwice a number decreased by 8 is 2 less than half the number.\u201d Step 1: Let the unknown number be […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-25192","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25192","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=25192"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25192\/revisions"}],"predecessor-version":[{"id":25193,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25192\/revisions\/25193"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}