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Equations with several steps

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

Now there are bags on both sides of the scale. You need several steps until \(x\) is on its own.
📄 Open worksheet (PDF, German)

The video

In the video we solve \(5x + 2 = 3x + 8\), first with the scale, then without it.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:01 Introduction
  2. 0:22 x on both sides
  3. 0:39 Numbers and dividing
  4. 0:57 Without the scale
  5. 1:23 Careful, mistake!
  6. 1:49 Try it yourself

The most important points

The order

1. All \(x\) to one side. 2. All numbers to the other side. 3. Divide. 4. Check.

5x + 2 = 3x + 8, | - 3x, | - 2, | : 2: x = 3.
\(5x + 2 = 3x + 8\), \(| - 3x\), \(| - 2\), \(| : 2\): \(x = 3\).

Without the scale it works the same way, also with minus: \(4x - 5 = 2x + 7\). \(| - 2x\): \(2x - 5 = 7\). \(| + 5\): \(2x = 12\). \(| : 2\): \(x = 6\).

First x to one side, then the numbers, then divide: x = 6.
First \(x\) to one side, then the numbers, then divide: \(x = 6\).
With - 5 you calculate + 5: always the opposite.
With \(- 5\) you calculate \(+ 5\): always the opposite.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
Page 1/3
The worksheet – Page 2
Page 2/3
Show the worksheet solutions
The worksheet – Page 3
Page 3/3

Try it yourself

Task

Solve: \(6x + 1 = 2x + 13\)

Show solution

\(| - 2x\): \(4x + 1 = 13\). \(| - 1\): \(4x = 12\). \(| : 4\): \(x = 3\).

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Gleichungen mit mehreren Umformungen (x auf beiden Seiten). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.