Numerical aptitude · Numbers
Equations, made easy
💡 The idea
An equation is a balance. Whatever you do to one side, do to the other side, and it stays balanced.
3x + 5 = 20→− 5 both sides→3x = 15→÷ 3 both sides→x = 5
🧭 The method: 3 steps
- Write the question as an equation (call the unknown x).
- Undo the + and − first, by doing the opposite to BOTH sides.
- Then undo the × and ÷. Check by putting x back in.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
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✏️ Worked examples
Example 1. 4x − 7 = 21
- + 7 to both sides: 4x = 28
- ÷ 4: x = 7
Example 2. Two numbers add to 50 and differ by 10. The bigger?
- Big + small = 50, big − small = 10
- Add: 2 × big = 60
- Big = 30
⚡ Shortcut: (sum + difference) ÷ 2.
Example 3. x² − 7x + 12 = 0
- Two numbers: × = 12, + = 7 → 3 and 4
- x = 3 or 4
⚠️ Where people go wrong
- Doing something to only one side.
- Undoing in the wrong order: + and − first, then × and ÷.
📌 Remember
- Same to both sides
- Bigger = (sum + diff) ÷ 2
- Smaller = (sum − diff) ÷ 2