# ‘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.

## Concept Practice

Write the sequence of operations needed to get back to the number $\,x\,$: