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Get ready for Algebra 1

Course: Get ready for Algebra 1 > Unit 1

Lesson 2: One-step addition & subtraction equations
Math
Get ready for Algebra 1
Get ready for equations & inequalities
One-step addition & subtraction equations
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One-step addition & subtraction equations

CCSS.Math:
6.EE.B.7
Google Classroom
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:
7, plus, 3, minus, 3, equals, 7
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:
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:
k+22=29k+22−22=29−22          Subtract 22 from each side.k=7          Simplify.\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 k+22=297+22=?2929=29\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:
p−18=3p−18+18=3+18          Add 18 to each side.p=21          Simplify.\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 p−18=321−18=?33=3\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
Choose 1 answer:
After applying the correct operation to each side, what is y?
y, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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  • blobby green style avatar for user m.sebi97
    Posted 5 years ago. Direct link to m.sebi97's post “An easyer way ive just di...”
    An easyer way ive just discovered is this:
    k + 22=29
    29-22=7
    k=7
    (81 votes)
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  • leaf blue style avatar for user KhanAcademyUser07
    Posted 2 years ago. Direct link to KhanAcademyUser07's post “why is there a pic of the...”
    why is there a pic of the queen of england
    (64 votes)
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  • mr pants purple style avatar for user alena.frausto
    Posted 3 years ago. Direct link to alena.frausto's post “so basically its always g...”
    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)
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  • aqualine sapling style avatar for user cheryl stroud
    Posted 3 years ago. Direct link to cheryl stroud's post “when you have h-3=15 then...”
    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)
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  • blobby green style avatar for user alexngan2028
    Posted a year ago. Direct link to alexngan2028's post “this guy basically took o...”
    this guy basically took over the us education system, pog
    (13 votes)
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  • leaf green style avatar for user renromero
    Posted 3 years ago. Direct link to renromero's post “It help and it helped me”
    It help and it helped me
    (11 votes)
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  • blobby green style avatar for user caiusrec.27256
    Posted 3 years ago. Direct link to caiusrec.27256's post “What is the easiest way t...”
    What is the easiest way to do this.
    (7 votes)
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    • female robot ada style avatar for user egg
      Posted 3 years ago. Direct link to egg's post “The easiest way to do thi...”
      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)
  • aqualine ultimate style avatar for user 24traben
    Posted 5 years ago. Direct link to 24traben's post “How do you solve a two-st...”
    How do you solve a two-step equations?
    (8 votes)
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    (8 votes)
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  • blobby green style avatar for user Jenna Le Brun Powell
    Posted 3 years ago. Direct link to Jenna Le Brun Powell's post “I was once shown how to d...”
    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)
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