One-step equations

Get the box alone

Guessing and checking works, but it's slow. There's a better way, and you can find it yourself.

Below, each box is an unknown weight $x$ and each circle weighs $1$. The scale is balanced. Your goal is to get one box alone on a pan, because then the other pan tells you exactly what it weighs. The only rule: keep the scale level.

Taking a weight off just one pan would tip the scale. To keep it level, you had to take the same amount off both pans. In symbols, you subtracted $3$ from both sides:

Splitting into groups

Now there are three boxes. You can't take boxes off, since there are none on the right. But you can split each pan into equal groups.

If three equal boxes balance $12$ weights, one box balances a third of them. Splitting into $3$ groups is dividing both sides by $3$:

Undo what was done

In both puzzles, you undid what had been done to $x$. Every operation has an inverse that undoes it:

If the variable is divided by a number, multiply both sides by it:

Negative numbers work the same way

A real scale can't hold a negative weight, but the rule still works: do the same thing to both sides.

Answers don't have to be whole numbers. If $3x = 2$, then $x = \frac{2}{3}$.

Key ideas

• Use the inverse operation to undo what was done to the variable.
• Do the same thing to both sides so the equation stays balanced.
• Check your answer by substituting it back into the original equation.