Balance Scale Equations

Pre-Algebra · Axiom Academy

An equation is a scale in balance An equals sign is a promise: the left side weighs exactly the same as the right. Picture a balance scale holding that promise. The moment you add weight to just one pan, the promise breaks and the scale tips. Everything you'll ever do to solve an equation comes from one rule that keeps that promise — and you can watch it happen first. Watch a balanced scale, 3 against 3. A single block drops onto the left pan and it tips — the two sides are no longer equal. Then the same block is added to the right, and the scale settles back to level. The fix for a tip is always: do the same thing to both sides. Add to one side and it tips; add the same to both and it stays level. That single move is the whole method. Now one pan holds a sealed box. We don't know its weight — call it x — but we know the scale must balance against the 5 on the right. Drag the weight hidden inside the box. The scale tips up while it's too light and down while it's too heavy; it sits level only when the box weighs exactly what the other side does. That balancing weight is the value of x . The scale balances at x = 5. Solving an equation just means finding the weight that keeps it level.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.