{"id":51,"date":"2023-06-26T18:31:12","date_gmt":"2023-06-26T18:31:12","guid":{"rendered":"https:\/\/physigeek.com\/nl\/duidelijke-formules\/"},"modified":"2023-06-26T18:31:12","modified_gmt":"2023-06-26T18:31:12","slug":"duidelijke-formules","status":"publish","type":"post","link":"https:\/\/physigeek.com\/nl\/duidelijke-formules\/","title":{"rendered":"Duidelijke formules"},"content":{"rendered":"<p>In dit artikel vindt u de regels voor het ophelderen van formules. Er wordt uitgelegd hoe je een formule oplost door een voorbeeld op te lossen en daarnaast kun je oefenen met stap-voor-stap opgeloste oefeningen om formules op te lossen. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Reglas-para-despejar-formulas\"><\/span>Regels voor het wissen van formules<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> De <strong>regels die worden gebruikt om de formules op te lossen<\/strong> zijn:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Als een term aan de ene kant van de formule wordt toegevoegd, kan deze worden doorgegeven door van de andere kant af te trekken.<\/span><\/li>\n<p style=\"text-align:center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-3d7866c0ef712774e421a5396fa6500e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A+B=C \\quad\\color{bleu}\\bm{\\longrightarrow}\\color{noir}\\quad A=CB\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"281\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Als een term aan de ene kant van de vergelijking wordt afgetrokken, kan deze worden doorgegeven door aan de andere kant toe te voegen.<\/span><\/li>\n<p style=\"text-align:center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-3bd660464775bec1eceeca0bce0a6533_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"AB=C \\quad\\color{bleu}\\bm{\\longrightarrow}\\color{noir}\\quad A=C+B\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"281\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Als een term \u00e9\u00e9n lid van de formule vermenigvuldigt, kan deze worden doorgegeven door het andere lid te delen.<\/span><\/li>\n<p style=\"text-align:center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-d7d4b6557587e426f2b88642db499a49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\\cdot (B+C)=D \\quad\\color{bleu}\\bm{\\longrightarrow}\\color{black}\\quad B+C=\\cfrac{D}{A}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"356\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Als een term een hele zijde van de formule verdeelt, kan deze worden doorgegeven door aan de andere kant te vermenigvuldigen.<\/span><\/li>\n<p style=\"text-align:center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-0df8def75421991fe6bdb88904276250_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{A+B}{C}=D \\quad\\color{bleu}\\bm{\\longrightarrow}\\color{noir}\\quad A+B=D\\cdot C\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"332\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Als een lid wordt verheven tot een exponent, kan het probleem worden opgelost door de wortel van die exponent in het andere lid te nemen.<\/span><\/li>\n<p style=\"text-align:center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-77c5387f7521ceec319a0c829f4041bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(A+B)^2=C+D \\quad\\color{bleu}\\bm{\\longrightarrow}\\color{noir}\\quad A+B=\\sqrt{C+D}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"412\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Als een hele zijde van een formule onder het teken van een wortel staat, kun je de wortel vinden door de andere zijde naar de index van de wortel te brengen.<\/span><\/li>\n<p style=\"text-align:center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a8c40f507cc69fecb09c4982caf1429a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{A+B}=C+D \\quad\\color{bleu}\\bm{\\longrightarrow}\\color{noir}\\quad A+B=(C+D)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"412\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/ul>\n<p> Samenvattend is de basisregel voor het oplossen van een formule dat om van kant te wisselen, een variabele aan de andere kant moet worden geplaatst door de omgekeerde bewerking uit te voeren.<\/p>\n<p> Deze regels vormen de basis voor het oplossen van formules in zowel de natuurkunde als de wiskunde, aangezien de procedure voor het isoleren van een variabele hetzelfde is, ongeacht de wetenschappelijke discipline.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Como-despejar-formulas\"><\/span> Hoe formules te wissen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Om een onbekende uit een formule op te lossen,<\/strong> moet je de regels voor het oplossen van formules toepassen, die erop neerkomen dat een term van kant kan veranderen door de omgekeerde bewerking uit te voeren.<\/p>\n<p> In het vorige gedeelte heb je alle wetten voor het oplossen van formules gedetailleerder uitgelegd.<\/p>\n<p> Houd er rekening mee dat termen die optellen en aftrekken normaal gesproken eerst moeten worden aangepast aan de kant van de formule, omdat het oplossen van producten, delingen, exponenten en wortels alleen kan worden gedaan als de bewerking wordt toegepast op de hele kant van de formule.<\/p>\n<p> Als u bijvoorbeeld variabele B uit de volgende formule wilt isoleren, geeft u eerst element C door aan de andere kant en deelt u vervolgens de gehele rechterkant door A:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-3d6dab6dcd6eef6d80c140e76b9fb87e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\\cdot B+C=D\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"115\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-500793e78870717abdd27cc11eb3d70c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\\cdot B=DC\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"93\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-5378828b72b438866c1597502005983a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B=\\cfrac{DC}{A}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"70\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Bovendien moeten haakjes worden gerespecteerd. Als een term bijvoorbeeld een haakje vermenigvuldigt en we een onbekende binnen de haakjes willen vinden, moeten we eerst de haakjes isoleren en vervolgens het onbekende erin oplossen.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-582675cbf6eea2cc6044e533b3ae3d9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\\cdot (B+C)=D\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-750303d20431978b8a5569b7aaea5aaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B+C=\\cfrac{D}{A}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"92\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-27bfdedff9ffb35b3e0011851c548305_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B=\\cfrac{D}{A}-C\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"91\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplo-de-despejar-una-formula\"><\/span> Voorbeeld van het verwijderen van een formule<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Om u te laten zien hoe u een variabele uit een formule wist, ziet u hieronder een concreet voorbeeld van het wissen van een formule.<\/p>\n<ul>\n<li> Los het onbekende op\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> uit de formule van de wet van Coulomb:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-0d441b62328166fe0550a6d0f8087728_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"F=K\\cfrac{q_1\\cdot q_2}{r^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"101\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> De voorwaarde<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-19db2644cdc31d7e9f0115deb1e187cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> verdeelt de gehele rechterkant van de formule, aangezien de volgende algebra\u00efsche uitdrukking equivalent is aan de vorige:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-98ca74d61e1c99a99ddd35905b8d775e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"F=\\cfrac{K\\cdot q_1\\cdot q_2}{r^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"113\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Daarom kunnen we de term vermenigvuldigen<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-4a367b9f68bd3041f6af61013a23b6a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r^2 par tout le c\u00f4t\u00e9 gauche.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"177\" style=\"vertical-align: -4px;\"><\/p>\n<p> Houd er rekening mee dat de zijkant moet worden vervangen met het vierkant erbij.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-b1508bf48ea48d8092e41723fc016b57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"F\\cdot r^2=K\\cdot q_1\\cdot q_2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> We kunnen nu de variabele doorgeven<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-88df03c55e081c7cd9da4e7d74ba7265_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"F\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> aan de andere kant van de delingsvergelijking omdat deze de hele linkerkant vermenigvuldigt:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a75476c44c45fa4632f4c4b17cf62ec3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" r^2=\\cfrac{K\\cdot q_1\\cdot q_2}{F}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"116\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> En ten slotte: om de exponent te verwijderen en de term te isoleren<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> je moet de vierkantswortel nemen van de rechterkant van de formule:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-e52261e36e3ac5586d20b086eaaf3049_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r=\\sqrt{\\frac{K\\cdot q_1\\cdot q_2}{F}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"128\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Op deze manier zijn we erin geslaagd de variabele uit de formule te verwijderen. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-despejar-una-formula\"><\/span> Problemen opgelost bij het wissen van een formule<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Hieronder laten we u verschillende opgeloste formule-verduidelijkingsoefeningen achter, zodat u kunt oefenen. Als je vragen hebt over een oefening of niet weet hoe je een vergelijking moet oplossen, onthoud dan dat je ons deze kunt stellen in de reacties hieronder.<\/p>\n<h3 class=\"wp-block-heading\"> Oefening 1<\/h3>\n<p> Los het onbekende op<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-816b613a4f79d4bf9cb51396a9654120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> uit de volgende formule: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-625a5d4e487d2f14df3bebf13bbb6338_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3C+2C(2A-5B)=7C+2B\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"239\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Zie de oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Eerst retourneren we het element<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-9105ff0742eac2ddd94cc9dce54b63e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3C\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\"><\/p>\n<p> om alleen de vermenigvuldiging aan de linkerkant te hebben. Omdat het een positief teken heeft, geven we het door aan het andere lid met een negatief teken:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-ec9fb68ff1e6d2fced78349655e77fbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2C(2A-5B)=7C+2B-3C\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"240\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We vereenvoudigen de rechterkant door te werken met de termen die dezelfde onbekende hebben:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-ff5503b2db7d7b97962ebd70450044f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2C(2A-5B)=4C+2B\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"195\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We hebben nu de term<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-526df3930d3759ad400fb2cbd3510482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2C\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\"><\/p>\n<p> vermenigvuldigd met de gehele linkerkant van de vergelijking, zodat we deze naar de rechterkant kunnen doorgeven door te delen:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-6cab840ff7ad89ea7579667fa800be47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2A-5B=\\cfrac{4C+2B}{2C}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"161\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We vereenvoudigen de breuk:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-98f75b26bc35e92b2988889e8b618c04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2A-5B=\\cfrac{2C+B}{C}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"152\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> De voorwaarde<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a6d86323c5b439cee2d0ebf006857883_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5B\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: 0px;\"><\/p>\n<p> aftrekt, veranderen we daarom het lid door op te tellen:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-b7872fb7fb79140113d9591ca6c8eaf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2A=\\cfrac{2C+B}{C}+5B\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"151\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ten slotte vermenigvuldigt de 2 alle elementen aan de linkerkant van de formule, zodat we dit kunnen doorgeven door alle elementen aan de andere kant te delen: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-bbd00e288b9ade469f5039113fec6cdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=\\cfrac{2C+B}{2C}+\\cfrac{5B}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"145\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Oefening 2<\/h3>\n<p> Wis de variabele<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> van de volgende formule: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-cacd0dcf6f32e96c45bc7132be078724_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f=\\cfrac{k\\cdot s}{sr}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"67\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Zie de oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Eerst geven we de noemer van de breuk door aan de andere kant door te vermenigvuldigen. Houd er rekening mee dat we deze stap kunnen uitvoeren omdat de noemer de hele rechterkant deelt:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-9549c76452d3af971638e290b3fcd01d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(sr)\\cdot f=k\\cdot s\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We verwijderen de haakjes:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-bd21ebd3e465aed9db35f14fbb3bf452_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\\cdot fr\\cdot f=k\\cdot s\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"118\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Nu plaatsen we alle elementen erbij<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> aan de ene kant van de vergelijking en de andere termen aan de andere kant:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-b127c9b7fca2b2f5c71937fa7d088784_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\\cdot fk\\cdot s=r\\cdot f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"118\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We extraheren de gemeenschappelijke factor in het linkerlid:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-c109d7612df40a8d9a780a71a583d9f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s(fk)=r\\cdot f\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> En ten slotte geven we de haakjes door die zich aan de andere kant van de vergelijking vermenigvuldigen door te delen: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-836b561c08f3954dab9c88992c487d36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s=\\cfrac{r\\cdot f}{fk}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"66\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Oefening 3<\/h3>\n<p> Wis de x uit de volgende vergelijking: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-87a5afee7f677cc4e65edcaa2cbfe4b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x-5y=4x+\\cfrac{7z-2x}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"184\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Zie de oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> In dit geval hebben we een term met x in de teller van een breuk, dus we zullen eerst het quoti\u00ebnt moeten oplossen om de noemer te kunnen verwijderen.<\/p>\n<p class=\"has-text-align-left\"> We gaan dus 4x naar de andere kant van de formule. Omdat je rechts optelt, ga je naar links door af te trekken:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-b14b29dafc238bc028a8e9d25a209a17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x-5y-4x=\\cfrac{7z-2x}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"184\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ten tweede geven we de delende 6 naar rechts door naar de andere kant door deze te vermenigvuldigen. We kunnen deze stap alleen uitvoeren als de deler alle termen aan \u00e9\u00e9n kant deelt, dus moesten we eerst van kant van de 4x wisselen.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-8e0fbbf24540272e5784e9d8101ebd12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6\\cdot (3x-5y-4x)=7z-2x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"217\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We lossen de vermenigvuldiging op:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-0c09ef91a301d0635afc4c1c1f46b17a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"18x-30y-24x=7z-2x\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"207\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We verplaatsen alle termen met x naar links en de andere elementen naar rechts:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-f9681102641ea780fbd3fa298f1cca7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"18x-24x+2x=7z+30y\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"207\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We voegen soortgelijke termen toe en trekken deze af:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-059c2ba4588a70a43c2ca4f5a184df34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-4x=7z+30y\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"122\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Om de x in de formule op te lossen, deelt u eenvoudigweg de co\u00ebffici\u00ebnt van x: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-bc35a4a9b13b8939e96885866540feb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{7z+30y}{-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"103\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Oefening 4<\/h3>\n<p> Isoleer de parameter<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-d6abdd487c56e5efbb2c9522ed4b9360_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"R\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> van de volgende formule: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-709c544afbec6f88dbe963d6e58f837a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P=\\cfrac{d+4K^2-\\frac{5}{\\sqrt{6R}}}{2T-5\\pi}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"158\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Zie de oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Eerst vermenigvuldigen we de termen die het andere lid van de formule verdelen:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-bee5644a057d236b8c77bbae0c994787_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2T-5\\pi)\\cdot P=d+4K^2-\\cfrac{5}{\\sqrt{6R}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"251\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We lossen de breuk aan de rechterkant op door de andere termen door te geven aan de andere kant door de omgekeerde bewerking uit te voeren:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-023157d53f67d0dfba90b67a80159360_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2T-5\\pi)\\cdot Pd-4K^2=-\\cfrac{5}{\\sqrt{6R}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"244\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> De wortel verdeelt de hele rechterkant van de formule, dus we geven deze door door de andere kant te vermenigvuldigen:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-82652554996a49888d7cc4c598154396_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{6R}\\cdot \\Bigl[(2T-5\\pi)\\cdot Pd-4K^2\\Bigr]=-5\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"279\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We verdelen de haakjes aan de andere kant:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-883536db0dd0af29916a3f1398d2558e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{6R}=\\cfrac{-5}{(2T-5\\pi)\\cdot Pd-4K^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"230\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> We kwadrateren de hele rechterkant van de formule om de vierkantswortel te verwijderen: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-5c96f1e288f3e5a3eb7a457396bb80f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 6R=\\left(\\frac{-5}{(2T-5\\pi)\\cdot Pd-4K^2}\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"250\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-d500886df35d319311821f4e5e2b8cad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 6R=\\frac{(-5)^2}{\\Bigl((2T-5\\pi)\\cdot Pd-4K^2\\Bigr)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"245\" style=\"vertical-align: -33px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-53bd41d659627408d95dca7d50c5f7f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 6R=\\frac{25}{\\Bigl((2T-5\\pi)\\cdot Pd-4K^2\\Bigr)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"245\" style=\"vertical-align: -33px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> En ten slotte geven we de co\u00ebffici\u00ebnt van de op te lossen parameter uit de formule door aan het andere lid: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-3948ad703728baa8e3d8c31840754a66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle R=\\frac{25}{6\\cdot \\Bigl((2T-5\\pi)\\cdot Pd-4K^2\\Bigr)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"257\" style=\"vertical-align: -33px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>In dit artikel vindt u de regels voor het ophelderen van formules. Er wordt uitgelegd hoe je een formule oplost door een voorbeeld op te lossen en daarnaast kun je oefenen met stap-voor-stap opgeloste oefeningen om formules op te lossen. Regels voor het wissen van formules De regels die worden gebruikt om de formules op &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/nl\/duidelijke-formules\/\"> <span class=\"screen-reader-text\">Duidelijke formules<\/span> Weiterlesen &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","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":"","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":"","footnotes":""},"categories":[17],"tags":[],"class_list":["post-51","post","type-post","status-publish","format-standard","hentry","category-vergelijkingen"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Formules oplossen (opgeloste oefeningen)<\/title>\n<meta name=\"description\" content=\"We leggen uit hoe u een formule verwijdert (regels voor het wissen van formules). 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