# Solving One-Step Equations

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:

## Example 1- One-step Multiplication Equations

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

## Example 2 - Working with Negative Numbers

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

## What Happens When 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.

## Example 3: Multiplication Equations with a Fraction Coefficient

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

## Example 4: Multiplication Equations

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

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