Solving Linear Equations: The Balance Scale

A linear equation is a statement that two expressions are equal. Solving means finding the value of $x$ that makes it true. The key principle: whatever you do to one side, do to the other — like a balance scale.

For $3x + 7 = 22$:

1. Subtract 7 from both sides: $3x = 15$
2. Divide both sides by 3: $x = 5$

Check: $3(5) + 7 = 15 + 7 = 22$ ✓

The balance-scale visualization makes this concrete: adding/removing weights from one side requires doing the same to the other side to keep the scale level.

Try it in the visualization

Adjust the coefficients $a$, $b$, $c$ in $ax + b = c$. The balance scale shows blocks on each side. Step through the solution — watch blocks get removed from both sides simultaneously. Toggle "show inverse operations" to see each algebraic step.