Home
#### Algebra and Pre-Algebra Lessons

Algebra 1 | Pre-Algebra | Practice Tests | Algebra Readiness Test
#### Algebra E-Course and Homework Information

Algebra E-course Info | Log In to Algebra E-course | Homework Calculator
#### Formulas and Cheat Sheets

Formulas | Algebra Cheat Sheets

Home > Solving Equations > Multiplication Equations

# Solving One-Step Equations

Multiplication Equations

### Solving one-step equations involving multiplication are easy as long as you can divide!

## Example 1

## Example 2

## Example 3

## Example 4

## Other Lessons You Might Like on Solving Equations

# Like This Page?

Multiplication Equations

The next set of one-step equations do not contain a constant that you must add or subtract to remove.

These equations contain a coefficient. A **coefficient** is a number that is multiplied by the variable.

Therefore, we must remove the coefficient. Take a look at this equation: **3x = 9.** Since there is no mathematical symbol between the 3 and the x
we know that means multiplication. So, what number times 3 will give us an answer of 9?

You know the answer, right? Yes, 3! **3*3 = 9**

Another question to ponder- What is the opposite of multiplication? Yes... division! We are going to divide in order to get x by itself!

Why divide? What is 3/3? Yes... 1! What is 1*x? You got it.... x! That's how we get x by itself.

We want the coefficient to be 1. Anytime you divide a number by itself, you will get an answer of 1!

Let's look at a few examples:

Pretty easy, huh? I think multiplication equations are even easier than addition and subtraction equations. Keep working, you'll get the hang of it!

Having trouble following this example? Take a look at the following video which will take you step by step through the same problem.

If you want to see this example on video, click here to visit my You Tube channel.

Not too hard if the coefficient is an integer! What happens if the coefficient is a fraction?

Think: If I have 2/3x, how can I make 2/3 a coefficient of 1?

Yes... you will divide by 2/3, but...Do you remember the term **reciprocal**? When you divide a fraction, you actually **multiply by the reciprocal**.

If you take 2/3 and you flip it to 3/2, that is the reciprocal! If you multiply by the reciprocal, you will have a coefficient of 1.

Watch this:

You may also have problems where your answer results in a fraction. Here's one more example:

Still confused, check out this example on the following video.

If you want to see this example on video, click here to visit my You Tube channel.

In this lesson, you learned a new vocabulary word, "coefficient" and hopefully you now have a better understanding of how to solve multiplication equations.

Solving Equations Unit

- Balancing Equations
- Solving one-step equations (Addition).
- Solving one-step equations (Subtraction).
- Solving one-step division equations.
- Solving two-step equations.
- Using the Distributive Property
- Solving equations with fractions
- Solving Literal Equations
- Equations with variables on both sides
- Writing equations given a word problem

Sign Up for Algebra Class E-courses

Click here to retrieve a lost password.

Custom Search

Dear Karin,

*I am a homeschool mom of five who struggled with finding a solid algebra program for my older boys until I came upon your algebra class. Your tutorials are straight forward and detailed. Your assignments are designed in such a way that we can spend extra time on what my children need to and move on when they understand something more easily.*

* I am a math-lover myself and am excited that you have finished part 2 of this course. My boys are understanding algebra in a way that they never were able to with other courses due to the detail and care that are in each of your lessons. I also appreciate that you are available to answer questions. *

Thank you,

Jacqui Coleman

Dear Karin,

*Finding your site was such a blessing to me! I
have been out of school for 13+ years and finding out that my next
course would be Algebra scared me to death!*

* I have now found a new
love of learning for algebra--something I never thought would happen.
After indulging in the section of functions, I decided to explore
other areas that I have just learned. It made areas such as
inequalities and graphing so much easier to grasp!*

* I just wanted to
thank you for your passion and dedication for helping others! I also
love the fact that you add in some humor, too. I have shared your site
with classmates and hope they take an opportunity to look into it as
well! Thank you----*

With greatest respect,

Dani

Hi Karin,

*I just spent 3 hours doing Unit 5 Lessons 1 & 2 because that is what I am learning at school this week, and cannot believe my progress. I so wish I would have found your course sooner. It is amazing. You explain everything in such clarity it's like night and day.
Thank you so much for getting me started. I am so happy you can't believe it.
You are the best instructor ever!*

Thanks again.

Joe

- FREE Solving Equations E-course
- Algebra Class E-course
- Algebra Class Products
- Algebra Practice Test
- Algebra Readiness Test
- Homework Answer Calculator
- Practice Worksheets

- Site Map
- Pre-algebra Refresher
- Solving Equations
- Graphing Equations
- Writing Equations
- Systems of Equations
- Inequalities
- Functions
- Exponents & Monomials
- Polynomials
- Quadratic Equations
- Algebra 1 Final Exam

- SAT Online Course
- Algebra Cheat Sheets - Very Popular!!
- Algebra Formulas
- Online Resources
- Contact Me
- I Want to Hear From You!
- Algebra Blog
- About Me

? ## Subscribe To This Site

Then why not use the button below, to add us to your favorite bookmarking service?

Copyright © 2009-2015 Karin Hutchinson ALL RIGHTS RESERVED

## Comments

We would love to hear what you have to say about this page!