Solving Equations Using Distributive Property

Instructor: Stephanie Matalone

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

In this lesson, we will go over the basics of the distributive property and how to use it. We will also talk about how to solve equations for a variable, particularly when those equations have parentheses in them.

Distributive Property

Before we talk about solving equations, let's first go over the distributive property. The distributive property involves the use of parentheses and explains how to multiply a number or term outside the parentheses with the numbers or terms inside the parentheses. For example, if you multiply 2 by (x + 1), you would use the distributive property to multiply the 2 by x and 1 separately. In the picture below, you can see how the 2 is distributed to each term. This is done by multiplying 2 by x to get 2x and multiplying 2 by 1 to get 2.

Anytime you see something outside parentheses with terms inside, you can distribute the outside term, no matter what the terms are or how many are present. This time, let's multiply y by (4y - 3x + 7). When doing this, we must use the distributive property to multiply y by each term inside the parentheses. We will multiply 4y by y, -3x by y and 7 by y. See the picture to visualize all this being done.

Solving Equations

When it comes time to solve an equation, all we are doing is figuring out what number the variable is equal to. A variable is a letter that represents an unknown value. Typically, we see variables as x or y, but they can be any letter in the alphabet.

So let's say we have the equation 2x + 3 = 7. In order to solve the equation, we want to see what number we can replace x with to make the equation true. In other words, what number can we plug in for x so the left side equals 7. In order to figure this out, we will use inverse operations or operations that undo one another. Addition and subtraction are inverse operations just like multiplication and division are inverse operations. To solve 2x + 3 = 7, we must get the x variable all alone. We will do this by moving everything to the right side of the equation with the 7. First, we must move the 3 over using the inverse operation of addition, which is subtraction. Then, we must move the 2 over using the inverse of multiplication which is division. Then, x is alone and equal to 2!

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