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Saxon Algebra 2 Homeschool: Online Textbook Help38 chapters | 297 lessons

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

There are several methods that can be used to solve equations. In this lesson, you'll learn about using the least common multiple method to help you combine and solve for your variable.

You might remember from your fraction days that the **least common multiple** (LCM), the lowest number that is a multiple of all your given numbers, is a number that can help you combine fractions. For example, to add 1/2 and 3/4, you have to find the least common multiple for the denominator before you could add these two fractions together like this.

- 1/2 + 3/4 = 2/4 + 3/4 = 5/4

The least common multiple for the denominator here is 4.

Well, you can use the least common multiple to help you solve your algebraic equations when you need to combine fractions to help you simplify your equations. To do this, follow these steps.

- Move all your variable terms to one side of the equation and all your constant terms to the other.
- Use the LCM to combine any fraction terms that are like terms.
- Continue solving for your variable by using your algebra skills.

Let's take a look at these steps in action now.

Let's solve this equation for the *x* variable.

Following the steps, you first move all your variable terms to one side. So pick one side, say the left side. Now move all the constant terms to the other side, the right side. Here is what it looks like.

Now, in the second step, combine your fractions with the help of the least common multiple. You are combining fractions, so your least common multiple will help you figure out what your denominators need to be before you can simplify this part of your equation.

You have 7 and 2 as denominators, so your least common multiple for these two numbers is 14. So you need to change both fractions so they both have a denominator of 14. Then you can combine them.

After using the LCM to help you combine fraction terms, continue solving for your variable using your algebra skills.

And you are done! Your answer is -28.

Let's look at another example and see if you can solve it on your own before reading the answer that follows.

This time, solve this equation for the unknown variable.

What's your first step? That's right, you move all your variable terms to one side and your constant terms to the other. Remember, it doesn't matter which side you choose as long as you keep them on opposite sides of the equal sign. This time, you can move your constants to the left side and your variables to the right side.

You have fractions, so now you need to use your least common multiple to help you combine your fractions.

Then, you finish your problem by using your algebra skills.

And you are done. Your answer is 156 / 7.

Let's review.

Your **least common multiple** (LCM) is the lowest number that is a multiple of all your given numbers.

To use it to help you solve algebraic equations, follow these steps.

- Move all your variable terms to one side of the equation and all your constant terms to the other.
- Use the LCM to combine any fraction terms that are like terms.
- Continue solving for your variable by using your algebra skills.

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8 in chapter 18 of the course:

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Saxon Algebra 2 Homeschool: Online Textbook Help38 chapters | 297 lessons

- Defining, Translating, & Solving One-Step Equations 6:15
- Simplifying & Solving Equivalent Equations
- Solving Equations Using the Addition Principle 5:20
- Solving Equations Using the Multiplication Principle 4:03
- How to Use the Fractional-Part-of-a-Number Equation
- Abstract Equation: Definition & Concept
- Simplifying & Solving Equations With Decimals & Mixed Numbers
- Solving Equations Using the Least Common Multiple
- Solving Addition Equations with Two or More Variables 7:57
- Solving Subtraction Equations with Two or More Variables 6:28
- How to Solve Equations with Multiple Steps 5:44
- Solving Multi-Step Equations with Multiple Variables
- Solving Equations Using Distributive Property
- Translating Words to Algebraic Expressions 6:31
- Direct and Inverse Variation Problems: Definition & Examples 6:27
- Solving Equations Involving Variation
- How to Solve a Rational Equation 7:58
- Solving Radical Equations with Two Radical Terms 6:00
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