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Solving equations: the scale

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

There are bags and weights on a scale. The scale is balanced. How heavy is one bag? This is how you learn to solve equations (Gleichungen).
📄 Open worksheet (PDF, German)

The video

In the video we take the same away on both sides of the scale. The scale stays balanced.

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

Contents of the video

  1. 0:01 Introduction
  2. 0:20 The equation
  3. 0:38 Taking away the same
  4. 0:54 Dividing and checking
  5. 1:27 Careful, mistake!
  6. 1:47 Try it yourself

The most important points

The equation

On the left 2 bags and 3 weights, on the right 11 weights: \(2x + 3 = 11\). The equals sign is like the middle of the scale.

One bag weighs x.
One bag weighs \(x\).

The same on both sides

Always do the same on both sides. \(| - 3\): \(2x = 8\). \(| : 2\): \(x = 4\).

3 weights away on both sides.
3 weights away on both sides.
Check (die Probe): 2 · 4 + 3 = 11 ✓
Check (die Probe): \(2 \cdot 4 + 3 = 11\) ✓

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 the equation \(3x + 2 = 14\). Do the check.

Show solution

\(| - 2\): \(3x = 12\). \(| : 3\): \(x = 4\). Check: \(3 \cdot 4 + 2 = 14\) ✓

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Gleichungen lösen mit der Waage (auf beiden Seiten dasselbe rechnen, Probe). 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.