audio read-through ‘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 $\,x\,$!

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

Remember some key ideas:

Concept Practice

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