‘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

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

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