Definition
Balance method
The balance method solves an equation by making the same reversible change to both whole sides.
What it means
Read the equals sign as “has the same value as.” First undo the operation joined to the unknown. Then make that same reversible change to the whole left side and the whole right side. The two sides stay equal, so the new equation keeps exactly the same solution.
Remember it
Picture a level beam: one move must reach both sides before the beam can stay level.
Example
To solve 3m = 21, divide the whole left side and the whole right side by 3. This gives m = 7. Check: 3 × 7 = 21, so 7 keeps the original equation true.
Watch for
From n + 4 = 10, erasing 4 only from the left and writing n = 10 changes the equation. Subtract 4 from both sides to keep an equivalent equation.
Common mix-up
The equals sign does not mean “the answer comes next.” It says the expressions on its two sides have the same value.
Exact meaning
The balance method solves an equation by applying the same reversible operation to both entire sides, producing an equivalent equation each time, until the unknown is isolated.