Practice Inverse Operations in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Operations that undo each other: addition undoes subtraction, multiplication undoes division, and vice versa. Applying an operation followed by its inverse returns you to the starting value.

Adding 5 then subtracting 5 brings you back to where you started.

Showing a random 20 of 50 problems.

Example 1

medium
Solve for xx: 7−x=27 - x = 2.

Example 2

challenge
Solve for xx: x−3=4\sqrt{x-3}=4.

Example 3

medium
I think of a number, multiply by 55, then subtract 44, and get 3636. What was my number?

Example 4

hard
A function machine doubles its input, then adds 33. If the output is 1919, find the input and explain the inverse machine.

Example 5

hard
Solve for xx: 3x+8=5x−43x + 8 = 5x - 4.

Example 6

medium
What is the inverse of subtracting 33 then dividing by 44? Give the steps in order.

Example 7

medium
Solve for xx: 2x+5=172x + 5 = 17.

Example 8

easy
What is the inverse operation of dividing by 6?

Example 9

easy
Fill in the blank: The inverse operation of cubing a number is taking the ___ root.

Example 10

medium
If f(x)=x+9f(x)=x+9, what input gives output 4?

Example 11

medium
A number divided by 4 equals 8. What is the number? Use inverse operations.

Example 12

medium
Maria has some marbles. She gives away 77, then her friend gives her 1515 more. She now has 3232. How many did she start with?

Example 13

easy
Start with 20. Subtract 7, then add 7. What is the result? What property does this show?

Example 14

medium
To find the side length of a square with area 8181 sq cm, what inverse operation undoes squaring?

Example 15

easy
Start with 12, add 7, then subtract 7. What is the result?

Example 16

hard
Solve for xx: x+7=5\sqrt{x + 7} = 5.

Example 17

medium
A number is multiplied by 3 and then 7 is added, giving 28. Find the number.

Example 18

medium
Solve for xx: 6(x−2)=306(x - 2) = 30.

Example 19

medium
You start with a mystery number. You multiply it by 6 and get 54. Use the inverse operation to find the mystery number.

Example 20

challenge
A machine doubles a number then subtracts 3; running its inverse on 11 gives what?
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