LESSON READ-THROUGH
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!

• PRACTICE (online exercises and printable worksheets)
• Need some basic practice with the connection between expressions and sequences of operations first?
  Going from an Expression to a Sequence of Operations
  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 $\,x\,$!

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

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.

CONCEPT QUESTIONS EXERCISE: On this exercise, you will not key in your answer. However, you can check to see if your answer is correct.

PROBLEM TYPES: 1 2 3 4 5 6 7 8 AVAILABLE MASTERED IN PROGRESS