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Equations with brackets

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

Three friends each buy a notebook and a pen. The pen costs 2 €. Together they pay 18 €. What does a notebook cost? The equation has a bracket: \(3 \cdot (x + 2) = 18\).
📄 Open worksheet (PDF, German)

The video

In the video we remove the bracket first. Then we go on as always.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:26 Expand first
  3. 0:55 A shorter way
  4. 1:11 x on both sides
  5. 1:37 Careful, mistake!
  6. 2:00 Try it yourself

The most important points

The bracket first

First expand: \(3x + 6 = 18\). Then \(| - 6\): \(3x = 12\). \(| : 3\): \(x = 4\).

Shorter: first | : 3, then x + 2 = 6.
Shorter: first \(| : 3\), then \(x + 2 = 6\).

Also with \(x\) on both sides: \(2 \cdot (x - 1) = x + 5\) becomes \(2x - 2 = x + 5\), so \(x = 7\).

Check: 2 · 6 = 12 and 7 + 5 = 12 ✓
Check: \(2 \cdot 6 = 12\) and \(7 + 5 = 12\) ✓
The 3 applies to both parts: 3x + 6, not 3x + 2.
The 3 applies to both parts: \(3x + 6\), not \(3x + 2\).

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 1/4
The worksheet – Page 2
Page 2/4
The worksheet – Page 3
Page 3/4
Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

Solve: a) \(5 \cdot (x - 2) = 15\) b) \(2 \cdot (x + 3) = x + 10\)

Show solution

a) \(5x - 10 = 15\), \(x = 5\) b) \(2x + 6 = x + 10\), \(x = 4\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Gleichungen mit Klammern (erst ausmultiplizieren, dann umformen). 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.