{"id":33291,"date":"2025-06-23T07:35:04","date_gmt":"2025-06-23T07:35:04","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=33291"},"modified":"2025-06-23T07:35:07","modified_gmt":"2025-06-23T07:35:07","slug":"how-many-solutions-does-3x-1-3x-1-have","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/how-many-solutions-does-3x-1-3x-1-have\/","title":{"rendered":"How many solutions does 3x \u2013 1 = 3x + 1 have"},"content":{"rendered":"\n<p>How many solutions does 3x \u2013 1 = 3x + 1 have?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Answer:<\/h3>\n\n\n\n<p>The equation <strong>3x \u2013 1 = 3x + 1<\/strong> has <strong>no solution<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To determine how many solutions this equation has, let us solve it step by step:<\/p>\n\n\n\n<p>The given equation is:<\/p>\n\n\n\n<p><strong>3x \u2013 1 = 3x + 1<\/strong><\/p>\n\n\n\n<p>The first step is to get all the terms involving <strong>x<\/strong> on one side and the constants on the other side. We can subtract <strong>3x<\/strong> from both sides:<\/p>\n\n\n\n<p><strong>3x \u2013 1 \u2013 3x = 3x + 1 \u2013 3x<\/strong><\/p>\n\n\n\n<p>This simplifies to:<\/p>\n\n\n\n<p><strong>\u20131 = 1<\/strong><\/p>\n\n\n\n<p>At this stage, we notice that the variable <strong>x<\/strong> has been eliminated from the equation, leaving us with:<\/p>\n\n\n\n<p><strong>\u20131 = 1<\/strong><\/p>\n\n\n\n<p>This is a <strong>false statement<\/strong> because negative one does not equal one.<\/p>\n\n\n\n<p>When solving an equation, if the variables cancel out and the result is a false statement, it means that <strong>no values of x<\/strong> will satisfy the equation. Therefore, the equation has <strong>no solution<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Why does this happen?<\/h3>\n\n\n\n<p>In this particular equation, both sides contain the term <strong>3x<\/strong>, which are identical. Subtracting <strong>3x<\/strong> from both sides removes all variable terms, leaving only constants. If those constants contradict each other, as in this case where <strong>\u20131 \u2260 1<\/strong>, the equation cannot be true for any value of <strong>x<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Types of outcomes in linear equations:<\/h3>\n\n\n\n<p>There are three possible outcomes when solving a linear equation:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>One unique solution<\/strong> \u2013 occurs when you isolate <strong>x<\/strong> and find a specific value.<\/li>\n\n\n\n<li><strong>No solution<\/strong> \u2013 occurs when variables cancel and the remaining statement is false.<\/li>\n\n\n\n<li><strong>Infinite solutions<\/strong> \u2013 occurs when variables cancel and the remaining statement is always true, like <strong>0 = 0<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p>Since we end up with <strong>\u20131 = 1<\/strong>, a false statement, the correct conclusion is:<\/p>\n\n\n\n<p><strong>No solution exists for the equation 3x \u2013 1 = 3x + 1.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-245.jpeg\" alt=\"\" class=\"wp-image-33292\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-245.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-245-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>How many solutions does 3x \u2013 1 = 3x + 1 have? The Correct Answer and Explanation is: Correct Answer: The equation 3x \u2013 1 = 3x + 1 has no solution. Explanation: To determine how many solutions this equation has, let us solve it step by step: The given equation is: 3x \u2013 1 [&hellip;]<\/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-33291","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33291","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=33291"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33291\/revisions"}],"predecessor-version":[{"id":33293,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33291\/revisions\/33293"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=33291"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=33291"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=33291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}