Definition:
Inverse Operations - Are opposite operations. Adding is the
inverse of subtracting and subtracting is the inverse of adding.
• The goal when solving equations is to isolate the variable.
• We isolate the variable by completing inverse operation(s).
• Remember, what you do to one side of the equation you
MUST do to the other!
Inverse Actions and Operations
What is the inverse of putting items in a box?
What is the inverse of tying your shoes?
What is the inverse of doing your homework?
What is the inverse of multiplication?
Example 1
x + 62 = 93
x + 62 = 93
- 62 - 62
x = 31
Check:
Example 2
81 = 17 + y
Original equation
Subtract 62 from BOTH
sides to isolate x.
Solution
Check your work
to see if your
answer is correct!
x + 62 = 93
Does 31 + 62 = 93?
93 = 93
Yes, it does
81 = 17 + y
- 17 – 17___
64 = y or
y = 64
Original equation
Subtract 17 from BOTH
sides to isolate y.
Solution
Check:
81 = 17 + y
Does 81 = 17 + 64?
81 = 81
Yes, it does
Check your work
to see if your
answer is correct!
Example 1
p–2=5
p–2=5
+2 +2
p=7
Example 2
40 = x - 11
Original equation
Add 2 to BOTH sides to
isolate p.
Solution
Check:
p-2=5
Does 7 - 2 = 5?
5=5
Yes, it does
Check your work
to see if your
answer is correct!
40 = x – 11
+ 11 + 11
51 = x or
x = 51
Original equation
Add 11 to BOTH sides to
isolate x.
Solution
Check:
40 = x - 11
Does 40 = 51 – 11?
40 = 40
Yes, it does
Check your work
to see if your
answer is correct!
Try these: Show all work and check your solutions.
1.) x + 16 = 90
2.) 21 = a + 13
3.) a - 33 = 49
4.) 45 = d - 11
Real-Life Application
Some surfers recommend that the length of a beginner’s surfboard
be 14 inches greater than the surfer’s height. If a surfboard is 82
inches, how tall should the surfer be to ride it? Set up and solve an
equation to find the answer.
Real-Life Application
When Theodore Roosevelt became president of the United States,
he was 42 years old. He was 27 years younger than Ronald Reagan
when Reagan became president. How old was Reagan when he
became president? Set up and solve an equation to find the
answer.