Determine whether the equation 3t+4=12+3t has one solution, no solution, or infinitely many solutions.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The equation ( 3t + 4 = 12 + 3t ) has infinitely many solutions<\/strong>. Here’s the step-by-step explanation:<\/p>\n\n\n\n We begin by simplifying the equation: Subtract ( 3t ) from both sides: At this point, we see that after simplifying the equation, we end up with a contradiction: ( 4 = 12 ). This suggests that there is an issue with the equation itself, specifically that the terms involving ( t ) have canceled out and left us with a false statement.<\/p>\n\n\n\n The fact that we reached a false statement like ( 4 = 12 ) after simplifying shows that the equation does not hold for any value of ( t ).<\/p>\n\n\n\n This means the equation has no solution<\/strong> because there’s no possible value of ( t ) that will satisfy the equation.<\/p>\n\n\n\n In summary:<\/p>\n\n\n\n In this case, the correct answer is no solution<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Determine whether the equation 3t+4=12+3t has one solution, no solution, or infinitely many solutions. The Correct Answer and Explanation is : The equation ( 3t + 4 = 12 + 3t ) has infinitely many solutions. Here’s the step-by-step explanation: Step 1: Simplify the equation We begin by simplifying the equation:[3t + 4 = 12 […]<\/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-169170","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/169170","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=169170"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/169170\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=169170"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=169170"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=169170"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Simplify the equation<\/h3>\n\n\n\n
[
3t + 4 = 12 + 3t
]
The goal is to isolate ( t ). To do this, let’s start by eliminating the ( 3t ) terms from both sides of the equation.<\/p>\n\n\n\nStep 2: Subtract ( 3t ) from both sides<\/h3>\n\n\n\n
[
3t + 4 – 3t = 12 + 3t – 3t
]
This simplifies to:
[
4 = 12
]
Now, we have a statement that is clearly false (4 does not equal 12).<\/p>\n\n\n\nStep 3: Analyze the result<\/h3>\n\n\n\n
Step 4: Conclusion<\/h3>\n\n\n\n
\n