衡 · Equations
Scroll of Balance
An equation is a scale in perfect balance. Whatever you do to one side, do to the other — and the unknown has nowhere to hide.
Mirror Move
Do the same thing to both sides. Remove what is added to x by subtracting it on both sides.
x + 7 = 15
- → Take 7 from both sides
- → x = 15 − 7
Answer: x = 8
Practice: Try x + 12 = 30 and x − 5 = 9.
Unwind the Form
Undo operations in reverse order: first the plus or minus, then the multiplication.
3x + 5 = 20
- → Remove +5: 3x = 15
- → Divide by 3: x = 5
Answer: x = 5
Brackets first? 4(x + 3) = 32 → divide by 4: x + 3 = 8 → x = 5.
Practice: Try 5x − 4 = 31 and 7(x − 6) + 6x = 101.
Gather the Clan
When x appears on both sides, move all x-terms to the side with more x, and all numbers to the other side.
6x − 1 = 5x + 2
- → Take 5x from both sides: x − 1 = 2
- → Add 1: x = 3
Answer: x = 3
Practice: Try 5x + 3 = 2x + 12. Check by putting your answer back in.
Into the dojo
Practise with the Balance ⚖ technique from green belt.