# ‘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.