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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:
• 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.

### 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.