"Undoing" a Sequence of Operations

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 $\,x\,$!

$x$	$\overset{\text{multiply by 2}}{\rightarrow}$	$2x$	$\overset{\text{add 1}}{\rightarrow}$	$2x + 1$
				$\,\downarrow\,$
$x$	$\overset{\text{divide by 2}}{\leftarrow}$	$2x$	$\overset{\text{subtract 1}}{\leftarrow}$	$2x + 1$

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.

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Solving for a Particular Variable


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

(MAX is 8; there are 8 different problem types.)