{"id":45874,"date":"2025-07-01T13:33:58","date_gmt":"2025-07-01T13:33:58","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=45874"},"modified":"2025-07-01T13:34:00","modified_gmt":"2025-07-01T13:34:00","slug":"graph-the-equation","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/graph-the-equation\/","title":{"rendered":"Graph the equation"},"content":{"rendered":"\n

Video Help [+] https\/\/www.xyzhomework.com\/imathas\/assess2\/?cid=37709&aid=2434513#\/skip\/2 ENTERING INTERVAL ANSWERS For intervals of values, enter your answer using interval notation. Here are some examples of how interval notation relates to inequalities: Inequality Interval Notation 3 < x < 5 (3,5) 3 ? x ? 5 [3,5] x ? 3 (3,?) 3 ? x ? 5 or 7 < x < 9 (3,5) U (7,9) With inequalities, we use “less than”: < or “greater than”: > to exclude the endpoint of the interval. With interval notation, we use use round parentheses, ( or ). With inequalities, we use “less than or equal to”: ? or “greater than or equal to”: ? to include the endpoint of the interval. With interval notation, we use use square brackets, [ or ]. To combine two intervals, use U (an uppercase letter u) for union: U Use oo (two lowercase letter o’s) for infinity, ? For example, to enter (-?, -2) U (3, 6], you would type: (-?,-2]U(3,6) Try it now. Enter the interval equivalent to 2 < x ? 5 or x > 7 Question Help:Message instructor Post to forum Submit 74<\/p>\n\n\n\n

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

To express the inequality 2<x\u226452 < x \\leq 52<x\u22645 or x>7x > 7x>7 in interval notation, we first break down the two conditions and understand how to write them as intervals:<\/p>\n\n\n\n

    \n
  1. For 2<x\u226452 < x \\leq 52<x\u22645<\/strong>:\n
      \n
    • The inequality says that xxx is strictly greater than 2 but less than or equal to 5.<\/li>\n\n\n\n
    • In interval notation, this translates to (2, 5]<\/strong>. The round parenthesis around 2 indicates that 2 is not included<\/strong> in the interval, and the square bracket around 5 indicates that 5 is included<\/strong>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • For x>7x > 7x>7<\/strong>:\n
        \n
      • This inequality states that xxx is strictly greater than 7.<\/li>\n\n\n\n
      • In interval notation, this is written as (7, \u221e)<\/strong>. The round parenthesis around 7 indicates that 7 is not included<\/strong> in the interval, and the infinity symbol \u221e\\infty\u221e is used to show that there is no upper limit to xxx, so it extends indefinitely.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

        Since these two inequalities are connected by “or,” we combine them using a union<\/strong> symbol \u222a\\cup\u222a. The union means that xxx can be in either of the two intervals.<\/p>\n\n\n\n

        Thus, the combined interval notation is:(2,5]\u222a(7,\u221e)(2, 5] \\cup (7, \\infty)(2,5]\u222a(7,\u221e)<\/p>\n\n\n\n

        Explanation:<\/h3>\n\n\n\n
          \n
        • (2, 5]<\/strong>: This represents the set of values of xxx that are greater than 2 and less than or equal to 5.<\/li>\n\n\n\n
        • (7, \u221e)<\/strong>: This represents the set of values of xxx that are greater than 7 and extend indefinitely.<\/li>\n\n\n\n
        • \u222a\\cup\u222a<\/strong>: The union symbol is used to show that xxx can be in either the first interval (2,5](2, 5](2,5] or the second interval (7,\u221e)(7, \\infty)(7,\u221e).<\/li>\n<\/ul>\n\n\n\n

          Therefore, the correct interval notation for 2<x\u226452 < x \\leq 52<x\u22645 or x>7x > 7x>7 is:(2,5]\u222a(7,\u221e)(2, 5] \\cup (7, \\infty)(2,5]\u222a(7,\u221e)<\/p>\n\n\n\n

          This format ensures clarity, representing all values of xxx that satisfy either condition.<\/p>\n\n\n\n

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

          Video Help [+] https\/\/www.xyzhomework.com\/imathas\/assess2\/?cid=37709&aid=2434513#\/skip\/2 ENTERING INTERVAL ANSWERS For intervals of values, enter your answer using interval notation. Here are some examples of how interval notation relates to inequalities: Inequality Interval Notation 3 < x < 5 (3,5) 3 ? x ? 5 [3,5] x ? 3 (3,?) 3 ? x ? 5 or 7 < […]<\/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-45874","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45874","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=45874"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45874\/revisions"}],"predecessor-version":[{"id":45876,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45874\/revisions\/45876"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=45874"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=45874"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=45874"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}