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Distributive Property for Multi-Step Equations

a(x + b) = c

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Distributive Property for Multi-Step Equations

How would you solve the equation 

Solving Multi-Step Equations Using the Distributive Property

When solving equations, it is often necessary for you to remove parentheses. The Distributive Property will help you do that.

Recall that the Distributive Property states:

Let's solve the following equations:

  1.  

Checking the solution:

Checking the solution:

  

 

 

Example

Example 1

Earlier, you were asked about how you could solve .

First, you need to remove the parentheses. You could use the Multiplication Property of Equality or the Distributive Property. Here, it is easier to use the Distributive Property.

Apply the Distributive Property:

Apply the Addition Property of Equality:

Simplify:

Apply the Multiplication Property of Equality:

The solution is .

Checking the solution:

Does Yes, so the answer is correct.

Example 2

Solve for when

Apply the Distributive Property:

Combine like terms:

Isolate the variable and its coefficient by using the Addition Property:

Isolate the variable by applying the Multiplication Property:

Checking your solution:

Substitute into

Therefore,

Review

In 1 – 22, solve the equation.

Review (Answers)

To see the Review answers, open this PDF file and look for section 3.5. 

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Vocabulary

distributive property

The distributive property states that the product of an expression and a sum is equal to the sum of the products of the expression and each term in the sum. For example, a(b + c) = ab + ac.

factor

Factors are the numbers being multiplied to equal a product. To factor means to rewrite a mathematical expression as a product of factors.

Variable

A variable is a symbol used to represent an unknown or changing quantity. The most common variables are a, b, x, y, m, and n.

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