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Lesson 4: One-step addition and 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:
$7+3-3=7$
Here's an example of how addition is the inverse operation of subtraction:
$5-2+2=5$

## Solving an addition equation using inverse operations

Let's think about how we can solve for $k$ in the following equation:
$\phantom{\rule{2em}{0ex}}k+22=29$
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:
$\phantom{\rule{2em}{0ex}}$ $\begin{array}{rl}k+22& =29\\ 7+22& \stackrel{?}{=}29\\ 29& =29\end{array}$
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:
$\phantom{\rule{2em}{0ex}}p-18=3$
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.

$\phantom{\rule{2em}{0ex}}$ $\begin{array}{rl}p-18& =3\\ 21-18& \stackrel{?}{=}3\\ 3& =3\end{array}$
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 equationExampleFirst step
Addition equation$k+22=29$Subtract 22 from each side.
Subtraction equation$p-18=3$Add 18 to each side.

## Let's try some problems.

Equation A
Which operation would help solve for $y$?
y+6=52
After applying the correct operation to each side, what is $y$?
$y=$

## Want to join the conversation?

• An easyer way ive just discovered is this:
k + 22=29
29-22=7
k=7
• just remember, this does not work for inequalities.
• why is there a pic of the queen of england
• I was wondering that to
• 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?
• pretty much
• Why is Queen Elizbeth on my screen?
• bc she is
• 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
• 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.
• It help and it helped me
• 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
• How do you solve a two-step equations?
• hello! just solve one that is the most easiest addition problem to you and then add the other number that seems a bit hard