Skill: Work backward from a result

To work backward, start with the known result and undo each operation in the reverse order. Use the inverse operation:

• Addition is undone by subtraction.
• Subtraction is undone by addition.
• Multiplication is undone by division.
• Division is undone by multiplication.

Example: A number is multiplied by $3$, and then $5$ is added. The result is $26$. What was the starting number?

The last operation was adding $5$, so undo it first:

$$26-5=21$$

The first operation was multiplying by $3$, so undo it next by dividing:

$$21\div 3=7$$

The starting number was $\boxed{7}$.

Check: Work forward from $7$:

$$7\times 3=21$$ $$21+5=26$$

The result matches, so the answer is correct.