{"content":[{"content":{"params":{"media":{"disableImageZooming":false},"text":"Trage die fehlenden W\u00f6rter ein.","overallFeedback":[{"from":0,"to":100}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["

Betrachte die folgenden Gleichungen und gib an, ob eine \u00c4qiivalenzumformung gemacht wurde und wenn ja, welche.<\/p>\n\n

Beispiel:<\/p>\n\n

-2x - 2 = 7x - 5<\/p>\n\n

-2 = 9x - 5<\/p>\n\n

\u00c4qivalenzumformung? Ja<\/p>\n\n

Welche Umformung? Addition von 2x<\/p>\n\n

1) 3x + 17 = -4 - 4x<\/p>\n\n

17 = -4 - 7x<\/p>\n\n

\u00c4qivalenzumformung? *Ja*<\/p>\n\n

Welche Umformung? *Subtraktion von 3x*<\/p>\n\n

2) 12 - 8x = -5x + 8<\/p>\n\n

12 = 3x + 8<\/p>\n\n

\u00c4quivalenzumformung? *Ja*<\/p>\n\n

Welche Umformung? *Addition von 8x*<\/p>\n\n

3) 3(b - 1) -7b = -5(-3 - 2b) +24<\/p>\n\n

-5(-3 - 2b) + 24 = 3(b - 1) - 7b<\/p>\n\n

\u00c4quivalenzumformung? *Nein*<\/p>\n\n

Welche Umformung? *Keine*<\/p>\n\n

4) 0,5x - 2 = 10<\/p>\n\n

x - 4 = 20<\/p>\n\n

\u00c4quivalenzumformung? *Ja*<\/p>\n\n

Welche Umformung? *Multiplikation mit 2*<\/p>\n\n

5) 27(x + 3) = 27<\/p>\n\n

(x + 3) = 1<\/p>\n\n

\u00c4quivalenzumformung? *Ja*<\/p>\n\n

Welche Umformung? *Division durch 27*<\/p>\n"]},"library":"H5P.Blanks 1.12","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Unbenannt: Fill in the Blanks"},"subContentId":"90d07aa3-fa78-4a12-98fc-e47a2fbe24a6"},"useSeparator":"auto"},{"content":{"params":{"media":{"disableImageZooming":false},"correct":"true","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false},"l10n":{"trueText":"Wahr","falseText":"Falsch","score":"Du hast @score von @total Punkten erreicht.","checkAnswer":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","wrongAnswerMessage":"Falsche Antwort","correctAnswerMessage":"Richtige Antwort","scoreBarLabel":"Du hast :num von :total Punkten erreicht."},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"

x = - 9\/7 ist die L\u00f6sung der Gleichung: 16 - 5x = 34 + 9x<\/p>\n"},"library":"H5P.TrueFalse 1.6","metadata":{"contentType":"True\/False Question","license":"U","title":"Unbenannt: True\/False Question"},"subContentId":"621e4256-c60a-4f30-8548-fb220e8889f1"},"useSeparator":"auto"},{"content":{"params":{"media":{"disableImageZooming":false},"correct":"false","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false},"l10n":{"trueText":"Wahr","falseText":"Falsch","score":"Du hast @score von @total Punkten erreicht.","checkAnswer":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","wrongAnswerMessage":"Falsche Antwort","correctAnswerMessage":"Richtige Antwort","scoreBarLabel":"Du hast :num von :total Punkten erreicht."},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"

x = 1,5 ist die L\u00f6sung der Gleichung: 15 - (5x + 8) = 19 + 3x<\/p>\n"},"library":"H5P.TrueFalse 1.6","metadata":{"contentType":"True\/False Question","license":"U","title":"Unbenannt: True\/False Question"},"subContentId":"bd93503d-ca0d-41b2-ab8c-63a4827d7222"},"useSeparator":"auto"},{"content":{"params":{"media":{"disableImageZooming":false},"correct":"true","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false},"l10n":{"trueText":"Wahr","falseText":"Falsch","score":"Du hast @score von @total Punkten erreicht.","checkAnswer":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","wrongAnswerMessage":"Falsche Antwort","correctAnswerMessage":"Richtige Antwort","scoreBarLabel":"Du hast :num von :total Punkten erreicht."},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"

x = 2\/5 ist die L\u00f6sung der Gleichung: 3(1 + 3x) - 4(x + 2) + 3 = 0<\/p>\n"},"library":"H5P.TrueFalse 1.6","metadata":{"contentType":"True\/False Question","license":"U","title":"Unbenannt: True\/False Question"},"subContentId":"d46e4d0e-5b81-43c5-8eed-5d816774c07c"},"useSeparator":"auto"},{"content":{"params":{"media":{"disableImageZooming":false},"correct":"false","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false},"l10n":{"trueText":"Wahr","falseText":"Falsch","score":"Du hast @score von @total Punkten erreicht.","checkAnswer":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","wrongAnswerMessage":"Falsche Antwort","correctAnswerMessage":"Richtige Antwort","scoreBarLabel":"Du hast :num von :total Punkten erreicht."},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"

x = 7\/27 ist die L\u00f6sung der Gleichung: 3 - 1,5x = 2x +5<\/p>\n"},"library":"H5P.TrueFalse 1.6","metadata":{"contentType":"True\/False Question","license":"U","title":"Unbenannt: True\/False Question"},"subContentId":"7dfe4bd6-06f5-4c32-92ce-4b17ba3c956a"},"useSeparator":"auto"},{"content":{"params":{"media":{"disableImageZooming":false},"text":"Trage die fehlenden W\u00f6rter ein.","overallFeedback":[{"from":0,"to":100}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["

Stelle zu den Zahlenr\u00e4tseln eine Gleichung auf und l\u00f6se diese.<\/p>\n\n

a) Welche Zahl muss man zu 2,75 addieren, um 0,3 zu erhalten?<\/p>\n\n

Gleichung: *x + 2,75 = 0,3*<\/p>\n\n

L\u00f6sung der Gleichung: *x = -2,45*<\/p>\n\n

b) Von welcher Zahl muss man 0,6 subtrahieren, um ihren ihren vierfachen Wert zu erhalten?<\/p>\n\n

Gleichung: *x - 0,6 = 4x*<\/p>\n\n

L\u00f6sung der Gleichung: *x = -0,2*<\/p>\n\n

c) F\u00fcr welche Zahl ist ihr F\u00fcnffaches um 1,8 gr\u00f6\u00dfer als ihre H\u00e4lfte?<\/p>\n\n

Gleichung: *5x = 0,5x + 1,8*<\/p>\n\n

L\u00f6sung der Gleichung: *x = 0,4*<\/p>\n"]},"library":"H5P.Blanks 1.12","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Unbenannt: Fill in the Blanks"},"subContentId":"7d7bed25-0a52-46ee-87e3-82e2f6f41f07"},"useSeparator":"auto"},{"content":{"params":{"media":{"disableImageZooming":false},"answers":[{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

x = -72\/35<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

x = 2<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

x = 0<\/div>\n"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"type":"auto","singlePoint":false,"randomAnswers":true,"showSolutionsRequiresInput":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"passPercentage":100,"showScorePoints":true},"UI":{"checkAnswerButton":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgainButton":"Wiederholen","tipsLabel":"Hinweis anzeigen","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","tipAvailable":"Hinweis verf\u00fcgbar","feedbackAvailable":"R\u00fcckmeldung verf\u00fcgbar","readFeedback":"R\u00fcckmeldung vorlesen","wrongAnswer":"Falsche Antwort","correctAnswer":"Richtige Antwort","shouldCheck":"H\u00e4tte gew\u00e4hlt werden m\u00fcssen","shouldNotCheck":"H\u00e4tte nicht gew\u00e4hlt werden sollen","noInput":"Bitte antworte, bevor du die L\u00f6sung ansiehst"},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"

Welche L\u00f6sung besitzt die Gleichung:<\/p>\n\n

1,2 +1,25x = 2\/3x<\/p>\n"},"library":"H5P.MultiChoice 1.14","metadata":{"contentType":"Multiple Choice","license":"U","title":"Unbenannt: Multiple Choice"},"subContentId":"1ad837b5-1213-4a5b-a499-0f9335494062"},"useSeparator":"auto"},{"content":{"params":{"media":{"disableImageZooming":false},"answers":[{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

x = -15<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

x = -16\/23<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

x = 0,5<\/div>\n"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"type":"auto","singlePoint":false,"randomAnswers":true,"showSolutionsRequiresInput":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"passPercentage":100,"showScorePoints":true},"UI":{"checkAnswerButton":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgainButton":"Wiederholen","tipsLabel":"Hinweis anzeigen","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","tipAvailable":"Hinweis verf\u00fcgbar","feedbackAvailable":"R\u00fcckmeldung verf\u00fcgbar","readFeedback":"R\u00fcckmeldung vorlesen","wrongAnswer":"Falsche Antwort","correctAnswer":"Richtige Antwort","shouldCheck":"H\u00e4tte gew\u00e4hlt werden m\u00fcssen","shouldNotCheck":"H\u00e4tte nicht gew\u00e4hlt werden sollen","noInput":"Bitte antworte, bevor du die L\u00f6sung ansiehst"},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"

Welche L\u00f6sung besitzt die Gleichung:<\/p>\n\n

2100x - 178(5x - 3) = 30(2x - 15) +184<\/p>\n"},"library":"H5P.MultiChoice 1.14","metadata":{"contentType":"Multiple Choice","license":"U","title":"Unbenannt: Multiple Choice"},"subContentId":"a9f0a29f-a3d7-446b-aecd-91cd9041f82d"},"useSeparator":"auto"},{"content":{"params":{"media":{"disableImageZooming":false},"answers":[{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

x = 1<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

x = 1,4<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

Welche L\u00f6sung hat die Gleichung:<\/p>\n\n

0 = 2,2x -0,2(8 - 2x) - 1,6(x - 1)<\/p>\n"},"library":"H5P.MultiChoice 1.14","metadata":{"contentType":"Multiple Choice","license":"U","title":"Unbenannt: Multiple Choice"},"subContentId":"621456f0-6455-42c0-9ad7-6c536d223a50"},"useSeparator":"auto"},{"content":{"params":{"media":{"disableImageZooming":false},"answers":[{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

x = 25<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

x = 10,5<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

x = -25<\/div>\n"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"type":"auto","singlePoint":false,"randomAnswers":true,"showSolutionsRequiresInput":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"passPercentage":100,"showScorePoints":true},"UI":{"checkAnswerButton":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgainButton":"Wiederholen","tipsLabel":"Hinweis anzeigen","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","tipAvailable":"Hinweis verf\u00fcgbar","feedbackAvailable":"R\u00fcckmeldung verf\u00fcgbar","readFeedback":"R\u00fcckmeldung vorlesen","wrongAnswer":"Falsche Antwort","correctAnswer":"Richtige Antwort","shouldCheck":"H\u00e4tte gew\u00e4hlt werden m\u00fcssen","shouldNotCheck":"H\u00e4tte nicht gew\u00e4hlt werden sollen","noInput":"Bitte antworte, bevor du die L\u00f6sung ansiehst"},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"

Welche L\u00f6sung hat die Gleichung:<\/p>\n\n

2,8x - 0,4(3x - 8) = 2x - 1,8 - 0,6x<\/p>\n"},"library":"H5P.MultiChoice 1.14","metadata":{"contentType":"Multiple Choice","license":"U","title":"Unbenannt: Multiple Choice"},"subContentId":"0957a173-4e1a-4492-bda3-a1d30b7fabd8"},"useSeparator":"auto"}]}

Lösen von Gleichungen