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Algebra (all content)

Course: Algebra (all content) > Unit 2

Lesson 4: One-step multiplication & division equations

One-step equations review

A one-step equation is an algebraic equation you can solve in only one step. You've solved the equation when you get the variable by itself, with no numbers in front of it, on one side of the equal sign.

What are one-step equations?

A one-step equation is an algebraic equation you can solve in only one step. Once you've solved it, you've found the value of the variable that makes the equation true.

To solve one-step equations, we do the inverse (opposite) of whatever operation is being performed on the variable, so we get the variable by itself. The inverse operations are:

Addition and subtraction
Multiplication and division

The most important thing to remember is that whatever you do to one side of the equation, you have to do the same thing to the other side.

Want to learn more about solving one-step equations? Check out this video.

Example: One-step equation with addition

Solve for k in the following equation:

k, plus, 18, equals, 21

We want to get k by itself on the left hand side of the equation. Right now k has 18 added to it, so we want to do the inverse and subtract 18 from both sides of the equation. Here's what that looks like:

\begin{aligned} k + 18 &= 21 \\\\ k + 18 \blueD{- 18} &= 21 \blueD{- 18}~~\small\gray{\text{Subtract 18 from each side.}} \\\\ k &= \greenD{3}~~\small\gray{\text{Simplify.}} \end{aligned}

Example: One-step equation with division

Solve for x in the following equation:

start fraction, x, divided by, 4, end fraction, equals, 6

We want to get x by itself on the left hand side of the equation. Right now x is being divided by 4, so we want to do the inverse and multiply by 4 on both sides of the equation. Here's what that looks like:

\begin{aligned} \dfrac x4 &= 6 \\\\ \dfrac x4 \cdot \blueD{4} &= 6 \cdot \blueD{4}~~\small\gray{\text{Multiply each side by four.}} \\\\ x &= \greenD{24}~~\small\gray{\text{Simplify.}} \end{aligned}

Practice

Problem 1

Current

Solve for k in the following equation:

k, minus, 7, equals, 16

k =

Want to try some more one-step equation problems? Check out this exercise.

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Alex L. : ( : | : )
Posted 6 years ago. Direct link to Alex L. : ( : | : )'s post “Why doesn't it have examp...”
Why doesn't it have example subtraction and multiplication.
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- chachi
  Posted 3 months ago. Direct link to chachi's post “The reason is because the...”
  The reason is because their is no inverse operation with subtraction and multiplication.
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Kevin Sotelo
Posted 3 years ago. Direct link to Kevin Sotelo's post “everthing is explained if...”
everthing is explained if you just proceed to the next lesson
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lizbeth
Posted 5 years ago. Direct link to lizbeth's post “why is there no example o...”
why is there no example of multiplication?
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Liana
Posted 4 years ago. Direct link to Liana's post “Can you please help my dd...”
Can you please help my dd is mad at me cause he thinks i cant do it.
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mcahill
Posted 6 months ago. Direct link to mcahill's post “why is this so easy”
why is this so easy
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lbad7370
Posted 3 years ago. Direct link to lbad7370's post “Why is it not saying I co...”
Why is it not saying I completed it?
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- Isaac Kassahun
  Posted 2 years ago. Direct link to Isaac Kassahun's post “A year late but better la...”
  A year late but better late then never. Did you try doing the questions at the bottom? That might be the reason why.
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adhrit.sachdeva
Posted 3 months ago. Direct link to adhrit.sachdeva's post “This is easy because this...”
This is easy because this is one step equation and you should try 2 step equations.
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TJ Coleman.
Posted 6 months ago. Direct link to TJ Coleman.'s post “I still don't understand”
I still don't understand
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- Mr. LaVallee
  Posted 23 days ago. Direct link to Mr. LaVallee's post “A one-step equation is an...”
  A one-step equation is an algebraic equation you can solve in only one step. Once you've solved it, you've found the value of the variable that makes the equation true. To solve one-step equations, we do the inverse (opposite) of whatever operation is being performed on the variable, so we get the variable by itself.
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Big Dane
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i need help with 3/7k-12/35
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Tramaine.C
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what is 8000341526354257635289845234x 561254376353759326596634672638027/
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