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Keep the balance: a mental math trick

When to use it: Solving any equation.

Worked example

Balancing 2x + 9 = 25A level balance: 2 x boxes and 9 dots on the left, 25 dots on the right. Take 9 from both sides: 2x = 16. Share 16 into 2 equal groups: x = 8.x8x888− 9− 92x + 9 = 252x = 16x = 82 × 8 + 9 = 25left sideright side
  1. Whatever you do to one side, do to the other.
  2. Undo in reverse order: in 2x + 9, the 9 came last, so take it away first.
  3. Check by putting the answer back in.

example Solve for x: 2x + 9 = 25

  1. Take 9 from both sides: 2x = 16.
  2. Divide both sides by 2: x = 8.
  3. Check: 2 × 8 + 9 = 25.

Answer: 8

Try three

  1. Solve for x: 9x + 12 = 66

    Show the answer

    x = 6

  2. Solve for x: 7x + 17 = 87

    Show the answer

    x = 10

  3. Solve for x: 9x + 3 = 84

    Show the answer

    x = 9

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Used in: Solve for the Unknown

More mental math tricks

This technique and its worked example are Doing Math’s own lesson text, checked by a blind re-solve and a review on September 27, 2026.