Undoing Operations: Inverses

≈ 20 min

Every basic operation has an inverse — an operation that undoes it:

Operation	Inverse
add $a$	subtract $a$
subtract $a$	add $a$
multiply by $a$	divide by $a$
divide by $a$	multiply by $a$

Solving equations is systematic undoing. In $x + 9 = 20$ , the $x$ has had 9 added to it. To free $x$ , apply the inverse — subtract 9 — from both sides:

x + 9 - 9 = 20 - 9 \;\Rightarrow\; x = 11

What is the inverse of adding 7?

Adding 7 again

Subtracting 7

Multiplying by 7

Dividing by 7

To undo multiplying by 5, you should…

multiply by 5

subtract 5

divide by 5

add 5

Use an inverse operation to solve: $x + 9 = 20$ .