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Lesson 3: 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, plus, 3, minus, 3, equals, 7
Here's an example of how addition is the inverse operation of subtraction:
5, minus, 2, plus, 2, equals, 5

Solving an addition equation using inverse operations

Let's think about how we can solve for k in the following equation:
k, plus, 22, equals, 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:
\begin{aligned} k + 22 &= 29 \\\\ k + 22 \blueD{- 22} &= 29 \blueD{- 22}~~~~~~~~~~\small\gray{\text{Subtract 22 from each side.}} \\\\ k &= \greenD{7}~~~~~~~~~~\small\gray{\text{Simplify.}} \end{aligned}

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:
p, minus, 18, equals, 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:
\begin{aligned} p - 18 &= 3 \\\\ p - 18 \blueD{+ 18} &= 3 \blueD{+ 18}~~~~~~~~~~\small\gray{\text{Add 18 to each side.}} \\\\ p &= \greenD{21}~~~~~~~~~~\small\gray{\text{Simplify.}} \end{aligned}

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 equationExampleFirst step
Addition equationk, plus, 22, equals, 29Subtract 22 from each side.
Subtraction equationp, minus, 18, equals, 3Add 18 to each side.

Let's try some problems.

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

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?
• yes. that is correct
• 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
• this guy basically took over the us education system, pog
• What is the easiest way to do this.
• 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.