Properties of Equality

Add/subtract the same number, or multiply/divide by the same non-zero number on both sides — the equality still holds

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About This Practice

An equation is a balanced scale: add or subtract the same weights on both sides and it stays level; multiply or divide both sides by the same non-zero number and it still stays level. Try it yourself: the equality survives only when both sides change the same way; change one side and the balance tips; and 0 can never be a divisor.

Run experiments on a balance: the left pan of x＋a＝b holds an x-box and weights, the right pan holds weights. Tap "+/−1 on both sides" or "divide both by the group count" and watch the balance stay level; change one side only and it tips at once; dividing by 0 is rejected — 0 can never be a divisor.

EasyEstimated Time: 10minproperties of equalitybalancelevelsolving equationsequation

How to Play

  1. Read the equation: an x-box and weights on the left pan, weights on the right — perfectly level.
  2. Tap "Both −1" and "Both +1": changing both sides keeps the balance and the equality.
  3. Tap "Left −1 only": the balance tips — changing one side alone breaks the equality.
  4. Switch to Rule 2: "Both ÷ count", "Both ÷2", "Both ×2" all stay level; "Both ÷0" is rejected.
  5. When x stands alone, read its value, then grab a new round.

Learning Objectives

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Properties of Equality - Expressions & Equations