Main content

## Operations and Algebraic Thinking 218-221

### Course: Operations and Algebraic Thinking 218-221 > Unit 5

Lesson 3: One-step addition & subtraction equations- One-step addition & subtraction equations
- One-step addition equation
- One-step addition & subtraction equations
- One-step addition & subtraction equations
- One-step addition & subtraction equations: fractions & decimals
- One-step addition & subtraction equations: fractions & decimals

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# One-step addition & subtraction equations

CCSS.Math:

Learn to solve equations like "x + 3 = 9" or "y - 5 = 8".

Based on our understanding of the balance beam model, we know that

*we always have to do the same thing to both sides of an equation to keep it true.*But how do we know

*what to do*to both sides of the equation?## Addition and subtraction are *inverse operations*

Inverse operations are opposite operations that undo or counteract each other.

Here's an example of how subtraction is the inverse operation of addition:

If we start with seven, add three, then subtract three, we get back to seven:

Here's an example of how addition is the inverse operation of subtraction:

If we start with five, subtract two, then add two, we get back to five:

## Solving an *addition* equation using inverse operations

Let's think about how we can solve for k in the following equation:

We want to get k by itself on the left hand side of the equation. So, what can we do to undo

*adding*22?We can

*subtract*22 because the inverse operation of addition is subtraction!Here's how subtracting 22 from each side looks:

### Let's check our work.

It's always a good idea to check our solution in the original equation to make sure we didn't make any mistakes:

$\qquad$ $\begin{aligned} k +22 &= 29 \\
\greenD{7} +22 &\stackrel{\large?}{=} 29\\
29 &= 29 \end{aligned}$

Yes, k, equals, start color #1fab54, 7, end color #1fab54 is a solution!

## Solving a *subtraction* equation using inverse operations

Now let's try to solve a slightly different type of equation:

We want to get p by itself on the left hand side of the equation. So, what can we do to cancel out

*subtracting*18?We can

*add*18 because the inverse operation of subtraction is addition!Here's how adding 18 to each side looks:

### Let's check our work.

$\qquad$ $\begin{aligned} p - 18 &= 3 \\
\greenD{21} - 18 &\stackrel{\large?}{=} 3\\
3 &= 3 \end{aligned}$

Yes, p, equals, start color #1fab54, 21, end color #1fab54 is a solution!

## Summary of how to solve addition and subtraction equations

Cool, so we just solved an addition equation and a subtraction equation. Let's summarize what we did:

Type of equation | Example | First step |
---|---|---|

Addition equation | k, plus, 22, equals, 29 | Subtract 22 from each side. |

Subtraction equation | p, minus, 18, equals, 3 | Add 18 to each side. |

## Let's try some problems.

## Want to join the conversation?

- An easyer way ive just discovered is this:

k + 22=29

29-22=7

k=7(80 votes)- just remember, this does not work for inequalities.(28 votes)

- why is there a pic of the queen of england(64 votes)
- I was wondering that to(29 votes)

- so basically its always gonna be the opposite of this like well minus is actually add and add is actually minus and times is actually division and division is actually times...right?(26 votes)
- when you have h-3=15 then you have to add 3 to the 15 and add the plus three to the negative three so what you would get is 18(14 votes)
- H - 3 = 15, We add 3 to both sides.

H - 3 + 3 = 15 + 3 The 3 cancels on the left side, and we get 18 on the right side.

H = 18

Your variable is equal to 18.(8 votes)

- this guy basically took over the us education system, pog(13 votes)
- It help and it helped me(11 votes)
- What is the easiest way to do this.(7 votes)
- The easiest way to do this is:

if we have 2+a=8

and we need to figure out "a" we can subtract 2 from 8, and that gives us 6, but in these problems we just need to figure out that with bigger numbers.

and for subtraction:

if we have the equation z-4=12

We can figure out "z" by adding 12 to 4 and that would be (16)"z" but in these problems we just do it with bigger numbers.(8 votes)

- How do you solve a two-step equations?(8 votes)
- hello! just solve one that is the most easiest addition problem to you and then add the other number that seems a bit hard(3 votes)

- I was once shown how to do this but slightly different - by transferring all of the numbers from one side of the equation to the other and changing them to their inverse, to isolate the variable you are trying to solve for...

Does this work for more complex equations involving multiplication and division and fractions etc?(6 votes)- Actually, your strategy is the same thing they are doing there, but it's more stretched out to seem more comprehensive. And yes, it does work for multiplication, division, and other complicated equations.(5 votes)

- I have and better way to just count up if you have big numbers than you can use this way so would i be able to do this way only for big numbers? this is harder the way you are doing it(8 votes)