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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

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

In algebra, when you want to solve an equation for a particular variable, you will need to perform multiple steps that include adding, subtracting, multiplying, and dividing. Watch this video lesson to learn the order you need to do these steps.

Many equations in algebra require you to perform multiple steps to solve for a particular variable. What this means is that you will need to perform more than one operation to solve the equation. This involves combining either addition or subtraction with either multiplication or division. Don't worry; it's not as difficult as it may sound. There's actually a method to solving these types of equations, and it's quite simple. Let's try solving one right now to see how easy it can be.

Let's solve the equation 4*x* + 3*x* - 7 = 0.

What do we do first? First, we **simplify** our equation by combining like terms. When we simplify our equation, we make sure that our equation is in its simplest form, which will save us time and make our work easier as we go on solving. We look at all our terms and notice that 4*x* and 3*x* are our like terms. The -7 is by itself with no other like terms, so we go ahead and combine the 4*x* and 3*x* by adding. Notice that when I look at the terms, if I notice a minus sign in front, then I keep that sign with my term so that I know that the term is a negative term. So, I combine my 4*x* and 3*x* to get 7*x*. I can now rewrite my equation with my combined like terms to get 7*x* - 7 = 0.

Next, we locate our variable. I see it being multiplied by the 7.

Now, you need to look for any addition or subtraction of numbers that is only happening on the same side as the side with our variable. If you see one of these operations, then you know that you need to move the number that is being added or subtracted. To do this, you perform the opposite operation. So, if you see addition, subtract, and if you see subtraction, add. I see a subtraction going on, so I am going to add. What is being subtracted? A 7 is being subtracted, so that tells me I need to add a 7. Remember in algebra, that to keep the equation the same, what you do to one side of an equation, you also must do the same to the other side. So if I add 7 to one side, I need to add a 7 to the other side as well. So I get 7*x* - 7 + 7 = 0 + 7, which turns into 7*x* = 7.

Why do we do addition and subtraction of numbers first? We do addition and subtraction first because this gets us closer to isolating our variable. What we are trying to do is to get closer and closer to our variable. We are working our way in to our variable. If we view our variable as being hidden inside a stack of boxes, we can view the addition and subtraction as opening the outermost box to get to our variable.

Next, we look to see if the variable is being multiplied or divided by anything. You can view this as opening the box that the variable is in. How do we do this? We do this the same way we did for the addition or subtraction. We do the opposite operation. So if we see multiplication, we will divide; if we see division, then we will multiply.

What do we see in our equation? We see our variable being multiplied by a 7. So, what do we do? We divide by 7 on both sides. Doing this, we get 7*x*/7 = 7/7 which turns into *x* = 1. We are done, and 1 is our answer. That wasn't so bad, was it?

Let's try another. Let's try solving 9*x* + 1 - 1 = 9.

What's our first step? It is to simplify our equation. The 1 and the -1 are like terms, so we can combine those. The 9 is by itself since it is on the other side of the equation, and nothing else is on that side. If there were other numbers on that side, then the 9 would have other like terms with which we could combine it. So, combining the 1 and -1 gives us 0, and our equation becomes 9*x* = 9.

Next, we identify or locate our variable. It is being multiplied by the 9.

Now, I look to see if there is any addition or subtraction of numbers on the same side as our variable. I don't see any.

Next, I look to see if the variable is being multiplied or divided by anything. I see the variable is being multiplied by 9. So I do the opposite operation and divide by 9 on both sides of the equation. Doing this, I get 9*x*/9 = 9/9, which turns into *x* = 1, and I am done. My answer is 1.

What have we learned? We've learned that solving equations that require multiple steps is not so hard. It starts with **simplifying** our equation, which means combining like terms. We then locate our variable. If there is any addition or subtraction of numbers on the same side as our variable, then we do the opposite operation to those numbers so that they move to the other side of the equation. This means if we see addition, then we subtract; if we see subtraction, then we add. We finish by seeing if the variable is being multiplied or divided by anything. If it is, then we perform the opposite operation again to isolate our variable. If there is multiplication, we divide; if there is division, we multiply.

After you've watched this lesson, you can apply your ability to:

- Remember the process of solving equations with multiple steps
- Work through provided examples using these steps

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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions 5:50
- Understanding and Evaluating Math Formulas 7:08
- Expressing Relationships as Algebraic Expressions 5:12
- Evaluating Simple Algebraic Expressions 7:27
- Combining Like Terms in Algebraic Expressions 7:04
- Practice Simplifying Algebraic Expressions 8:27
- Negative Signs and Simplifying Algebraic Expressions 9:38
- Writing Equations with Inequalities: Open Sentences and True/False Statements 4:22
- Common Algebraic Equations: Linear, Quadratic, Polynomial, and More 7:28
- Defining, Translating, & Solving One-Step Equations 6:15
- Solving Equations Using the Addition Principle 5:20
- Solving Equations Using the Multiplication Principle 4:03
- Solving Equations Using Both Addition and Multiplication Principles 6:21
- Collecting Like Terms On One Side of an Equation 6:28
- Solving Equations Containing Parentheses 6:50
- Solving Equations with Infinite Solutions or No Solutions 4:45
- Translating Words to Algebraic Expressions 6:31
- How to Solve One-Step Algebra Equations in Word Problems 5:05
- How to Solve Equations with Multiple Steps 5:44
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- Go to High School Algebra: Algebraic Expressions and Equations

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