QUICK LINKS


Introduction

QUICK LINKS


Introduction

Inverse Operations in One Step Equations

INTRO
β€”
An equation is a math sentence that uses an equals sign to tell us two values or expressions are equal.
The equation below reads, is equal to .
The is a variable, which is a symbol that represents a number or value we don’t know yet but want to find.
When there is only one operation acting on the variable, we call the equation a one step equation, meaning it only requires one inverse operation to solve for the value of the variable.
Just like how an antidote undoes the effect of poison, the inverse operation () undoes the effect of the operation () acting on the variable we’re solving for.
To undo , we use division.
When we use an inverse operation on one side of the equation, we have to do the same thing on the other side to keep the equation balanced.
Think of this as applying the antidote to both sides to clear out the poison completely.
CALCULATOR
β€”
What variable are you solving for?

Step 1. Identify the operation on the variable.

This is what’s being done to the variable - think of it as the poison.
operation: add

Step 2. Identify the inverse operation.

The opposite of addition is subtraction - think of the inverse operation as the antidote.
operation
add
inverse
subtract

Step 3. Undo with the inverse operation.

Think of this as applying the antidote to both sides to clear out the poison completely.
So, our answer is
.
KEY STEPS
β€”

How to Solve One Step Equations

Step 1. Identify the operation on the variable.

This is what’s being done to the variable - think of it as the poison.

Step 2. Identify the inverse operation.

Think of the inverse operation as the antidote.
OperationInverse
Add Subtract
Subtract Add
Multiply Divide
Divide Multiply
A power A root
A root A power

Step 3. Undo with the inverse operation.

Think of this as applying the antidote to both sides to clear out the poison completely.
LESSON
β€” Solving One Step Equations

Solving One Step Equations

When it only takes a single inverse operation to isolate the variable, we call the equation a one-step equation.

The inverse operation works to undo the effect of the operation acting on the variable, just like how an antidote undoes the effect of a poison.

To undo , we use division.

By getting rid of the operation/poison completely on both sides, we can solve for the variable.

What does it mean to keep an equation balanced?

Keeping an equation balanced means making sure that the equation stays true as we change it.

Whatever we do to one side of the equation, also needs to be done to the other side of the equation. Otherwise, the equation will no longer be balanced (true).

Balanced (True)Not Balanced (False)
Let’s walk through some step-by-step examples of how to solve one step equations!

EXAMPLE 1

Let's start by using inverse operations to solve for :

EXAMPLE 2

Nice work! Now, let's solve for :

EXAMPLE 3

Amazing! Next, let's solve for :

EXAMPLE 4

Great! Next, let's solve for :

EXAMPLE 5

Incredible work! Now, let's solve for :

EXAMPLE 6

Incredible work! Last one - let's solve for :
Awesome! If you’d like to practice additional problems with solving one step equations, expand the
Practice
below before closing out this lesson! ⚑
PRACTICE
β€” Solving One Step Equations

Practice: Solving One Step Equations

Question 1 of 10: Solve for .

Step 1. Identify the operation on the variable.

This is what’s being done to the variable - think of it as the poison.
operation:

Step 2. Identify the inverse operation .

is the opposite of addition - think of the inverse operation as the antidote.
operation
add 4
inverse

Step 3. Undo with the inverse operation.

Think of this as applying the antidote to both sides to clear out the poison completely.
Drag the inverse operation to both sides of the equation:
Awesome job! The final answer is Β .

CONCLUSION
β€”
Dang, look at you go! Thanks for checking out this lesson β˜ΊοΈπŸ™. Where to next?
Leave Feedback