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

Example 2

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 what a reciprocal is in math? 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:

Example 3

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

Example 4

Solving One-step Equations Practice

Ok.... ready to check your answers?

One-Step Equations Answer Key

Return to Algebra Class Home Page.