how do you solve 2 – 2n = 3n + 17<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n Let’s solve the equation step-by-step:<\/p>\n\n\n\n Equation:<\/strong> We want to gather all terms involving nn on one side and constants on the other.<\/p>\n\n\n\n Add 2n2n to both sides to move \u22122n-2n to the right: 2=3n+17+2n2 = 3n + 17 + 2n<\/p>\n\n\n\n Simplify the right side: 2=5n+172 = 5n + 17<\/p>\n\n\n\n Subtract 17 from both sides: 2\u221217=5n+17\u2212172 – 17 = 5n + 17 – 17 \u221215=5n-15 = 5n<\/p>\n\n\n\n Divide both sides by 5: \u2212155=n\\frac{-15}{5} = n n=\u22123n = -3<\/p>\n\n\n\n n=\u22123\\boxed{n = -3}<\/p>\n\n\n\n This is a linear equation in one variable, nn. The goal is to isolate nn on one side of the equation so we can find its value.<\/p>\n\n\n\n The original equation is 2\u22122n=3n+172 – 2n = 3n + 17. Here, 22 and 1717 are constants, while \u22122n-2n and 3n3n are terms with nn.<\/p>\n\n\n\n First, we want to collect all nn terms on one side to simplify the equation. Adding 2n2n to both sides eliminates the \u22122n-2n from the left, combining like terms on the right: 2=3n+17+2n2 = 3n + 17 + 2n<\/p>\n\n\n\n Simplifying the right side gives: 2=5n+172 = 5n + 17<\/p>\n\n\n\n Next, we move the constant term 1717 to the left side by subtracting 17 from both sides, isolating the term with nn: 2\u221217=5n2 – 17 = 5n \u221215=5n-15 = 5n<\/p>\n\n\n\n Finally, to solve for nn, divide both sides by the coefficient of nn, which is 5: n=\u2212155=\u22123n = \\frac{-15}{5} = -3<\/p>\n\n\n\n The solution means that when n=\u22123n = -3, both sides of the original equation are equal.<\/p>\n\n\n\n You can verify this by substituting n=\u22123n = -3 back into the original equation:<\/p>\n\n\n\n Left side: 2\u22122(\u22123)=2+6=82 – 2(-3) = 2 + 6 = 8 Since both sides equal 8, n=\u22123n = -3 is the correct solution.<\/p>\n","protected":false},"excerpt":{"rendered":" how do you solve 2 – 2n = 3n + 17 The correct answer and explanation is: Let’s solve the equation step-by-step: Equation:2\u22122n=3n+172 – 2n = 3n + 17 Step 1: Get all terms with nn on one side We want to gather all terms involving nn on one side and constants on the other. […]<\/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-24786","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24786","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=24786"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24786\/revisions"}],"predecessor-version":[{"id":24790,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/24786\/revisions\/24790"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=24786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=24786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=24786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
2\u22122n=3n+172 – 2n = 3n + 17<\/p>\n\n\n\n
\n\n\n\nStep 1: Get all terms with nn on one side<\/h3>\n\n\n\n
\n\n\n\nStep 2: Isolate the term with nn<\/h3>\n\n\n\n
\n\n\n\nStep 3: Solve for nn<\/h3>\n\n\n\n
\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
\n\n\n\nExplanation (300 words):<\/h3>\n\n\n\n
Right side: 3(\u22123)+17=\u22129+17=83(-3) + 17 = -9 + 17 = 8<\/p>\n\n\n\n