Solving a Linear Equation Step‑by‑Step

Overview

A slow, pedagogical animation that writes out each algebraic manipulation of the equation $2x + 3 = 4$ character‑by‑character. The teacher can pause after any line to explain the transformation. The final solution is highlighted and held on screen.

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Phases

#	Phase Name	Duration	Description
1	Display Problem	~4 s	The problem $2x + 3 = 4$ fades in at the top of the screen.
2	Write First Line	~14 s	Characters of $2x + 3 = 4$ appear one‑by‑one (2 s per character) with a blinking cursor.
3	Pause 1	~4 s	All written lines stay visible; teacher may pause.
4	Write Second Line	~10 s	Characters of the transformed equation $2x = 1$ appear sequentially; the moved “‑3” is highlighted in a subtle orange glow.
5	Pause 2	~4 s	Screen holds the two lines.
6	Write Third Line	~10 s	Characters of $x = \frac{1}{2}$ appear; the division by 2 is highlighted in teal.
7	Pause 3	~4 s	All three lines remain on screen.
8	Final Answer Emphasis	~6 s	The final line $x = \frac{1}{2}$ is recolored to bright blue and a gentle glow surrounds it. It stays for at least 5 s before the scene ends.
9	Outro	~2 s	Fade out to a blank board.

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Layout

┌─────────────────────────────────────────────┐
│                 TOP AREA                    │  ← Problem statement (large font)   
├─────────────────────────────────────────────┤
│                 MAIN AREA                    │  ← Step‑by‑step equations, left‑aligned
│                                             │
│   2x + 3 = 4                                 │
│   2x = 1                                    │
│   x = \frac{1}{2}                           │
│   x = \frac{1}{2}   (highlighted)          │
│                                             │
├─────────────────────────────────────────────┤
│                BOTTOM AREA                  │  ← Optional small caption (e.g., "Solution")
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	The original problem $2x + 3 = 4$	Fades in at Phase 1; large, high‑contrast font
Main	Each equation line as it is written	Left‑aligned, LaTeX‑styled; previous lines remain visible
Bottom	Optional caption like “Solution” (small font)	Fades in with the final answer

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Notes

• Background: Dark chalk‑board style (deep charcoal) with a faint texture to mimic a classroom board.
• Font: A clean, sans‑serif math font (e.g., Computer Modern or Latin Modern) at a size that is easily readable from the back of a classroom.
• Character Timing: Exactly 2 seconds per character, including spaces and operators. A blinking cursor appears at the insertion point while characters are being written.
• Highlighting: When a term is moved or an operation is performed, that term glows (orange for subtraction, teal for division) for the duration of the line’s appearance.
• Pauses: Each pause is a random duration between 3 s and 5 s (set to 4 s for the spec) to give the teacher a natural moment to speak.
• Final Hold: The final answer line stays on screen for at least 5 seconds before the fade‑out.
• Single Scene: All phases occur within one Manim Scene class.
• No extra text: Apart from the equations and optional small caption, no explanatory text is displayed; the visual progression conveys the solution.