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