How to Solve Equations with Multiple Steps

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  • 0:01 Solving Equations with…
  • 1:35 Adding and Subtracting First
  • 2:58 Multiplying and…
  • 3:43 A Second Example
  • 4:55 Lesson Summary
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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.

Solving Equations with Multiple 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 4x + 3x - 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 4x and 3x are our like terms. The -7 is by itself with no other like terms, so we go ahead and combine the 4x and 3x 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 4x and 3x to get 7x. I can now rewrite my equation with my combined like terms to get 7x - 7 = 0.

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

Adding and Subtracting First

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 7x - 7 + 7 = 0 + 7, which turns into 7x = 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.

Multiplying and Dividing Second

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.

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