‘Undoing’ a Sequence of Operations
Need some basic practice with the connection between expressions and sequences of operations first? Going from an Expression to a Sequence of Operations and Going from a Sequence of Operations to an Expression
In this exercise, you will practice ‘undoing’ operations.
The expression $\,2x + 1\,$ represents the sequence of operations: start with a number $\,x\,,$ multiply by $\,2\,,$ then add $\,1\,.$
To ‘undo’ these operations and get back to $\,x\,,$ we must apply the sequence: subtract $\,1\,,$ then divide by $\,2\,.$
Start with $\,x\,$ and follow the arrows in the diagram below. This shows you doing something, and then undoing it, to return to $\,x\,$!
| $x$ | $\overset{\quad\text{multiply by 2}\quad}{\rightarrow}$ | $2x$ | $\overset{\text{add 1}}{\rightarrow}$ | $2x + 1$ |
| $\,\downarrow\,$ | ||||
| $x$ | $\overset{\text{divide by 2}}{\leftarrow}$ | $2x$ | $\overset{\quad\text{subtract 1}\quad}{\leftarrow}$ | $2x + 1$ |
Remember some key ideas:
- Whatever you do last must get ‘undone’ first.
- More generally, whatever you do, you must ‘undo’ in reverse order.
- How do you undo ‘add $\,1\,$’? Answer: Subtract $\,1\,.$ Addition is undone with subtraction, and vice versa.
- How do you undo ‘multiply by $\,2\,$’? Answer: Divide by $\,2\,.$ Multiplication is undone with division, and vice versa.