John was given the equation 4(2a + 3)= -3(a – 1) + 31 – 11. Some steps an their reasons have already been completed. State a property of numbers for each missing reason.<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n Let’s solve the equation step by step and identify the missing properties of numbers for each step. The original equation is:<\/p>\n\n\n\n [ Distribute the ( 4 ) on the left side of the equation:<\/p>\n\n\n\n [ This is an application of the distributive property<\/strong>, which states that for any numbers ( a ), ( b ), and ( c ), we have:<\/p>\n\n\n\n [ So, the equation becomes:<\/p>\n\n\n\n [ Next, distribute the ( -3 ) on the right side of the equation:<\/p>\n\n\n\n [ The equation now becomes:<\/p>\n\n\n\n [ Now, simplify the constants on the right side of the equation:<\/p>\n\n\n\n [ So, the equation becomes:<\/p>\n\n\n\n [ This step involves combining like terms<\/strong> (specifically, the constants on the right side). The property involved here is the associative property of addition<\/strong>, which states:<\/p>\n\n\n\n [ Now, we add ( 3a ) to both sides to move the ( a )-terms to one side:<\/p>\n\n\n\n [ This is an application of the additive property of equality<\/strong>, which states that if ( a = b ), then ( a + c = b + c ) for any ( c ). Here, ( 8a + 3a = 11a ), and we get:<\/p>\n\n\n\n [ Next, subtract ( 12 ) from both sides:<\/p>\n\n\n\n [ This step also involves the additive property of equality<\/strong>, where subtracting the same value from both sides keeps the equation balanced.<\/p>\n\n\n\n So we now have:<\/p>\n\n\n\n [ Finally, divide both sides by ( 11 ) to solve for ( a ):<\/p>\n\n\n\n [ This is an application of the multiplicative inverse property<\/strong>, which states that for any number ( a ), if ( a \\neq 0 ), then:<\/p>\n\n\n\n [ The solution to the equation is ( a = 1 ).<\/p>\n","protected":false},"excerpt":{"rendered":" John was given the equation 4(2a + 3)= -3(a – 1) + 31 – 11. Some steps an their reasons have already been completed. State a property of numbers for each missing reason. The Correct Answer and Explanation is: Let’s solve the equation step by step and identify the missing properties of numbers for each […]<\/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-167288","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167288","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=167288"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167288\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167288"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167288"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167288"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
4(2a + 3) = -3(a – 1) + 31 – 11
]<\/p>\n\n\n\nStep 1: Apply the distributive property<\/h3>\n\n\n\n
4 \\times (2a + 3) = 4 \\times 2a + 4 \\times 3 = 8a + 12
]<\/p>\n\n\n\n
c(a + b) = ca + cb
]<\/p>\n\n\n\n
8a + 12 = -3(a – 1) + 31 – 11
]<\/p>\n\n\n\nStep 2: Apply the distributive property again on the right side<\/h3>\n\n\n\n
-3(a – 1) = -3 \\times a + (-3) \\times (-1) = -3a + 3
]<\/p>\n\n\n\n
8a + 12 = -3a + 3 + 31 – 11
]<\/p>\n\n\n\nStep 3: Simplify constants on the right side<\/h3>\n\n\n\n
3 + 31 – 11 = 23
]<\/p>\n\n\n\n
8a + 12 = -3a + 23
]<\/p>\n\n\n\n
a + (b + c) = (a + b) + c
]<\/p>\n\n\n\nStep 4: Move terms involving ( a ) to one side<\/h3>\n\n\n\n
8a + 3a + 12 = 23
]<\/p>\n\n\n\n
11a + 12 = 23
]<\/p>\n\n\n\nStep 5: Move constants to the other side<\/h3>\n\n\n\n
11a = 23 – 12
]<\/p>\n\n\n\n
11a = 11
]<\/p>\n\n\n\nStep 6: Solve for ( a )<\/h3>\n\n\n\n
a = \\frac{11}{11} = 1
]<\/p>\n\n\n\n
\\frac{a}{a} = 1
]<\/p>\n\n\n\nSummary of properties used:<\/h3>\n\n\n\n
\n