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### Course: Algebra (all content) > Unit 2

Lesson 3: One-step addition & subtraction equations# One-step addition & subtraction equations

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:

Yes, $k={7}$ 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.

Yes, $p={21}$ 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 | Subtract 22 from each side. | |

Subtraction equation | Add 18 to each side. |

## Let's try some problems.

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