Suppose you were a contestant on a game show where they gave you the answer and you had to think of the corresponding question. If the answer were, " or ," what would you give for the question? How about, "What is the Distributive Property?" In this Concept, you will learn all about the Distributive Property and how to use it to solve equations with multiple steps.

### Guidance

**Solving Multi-Step Equations by Using the Distributive Property**

When faced with an equation such as , the first step is to remove the parentheses. There are two options to remove the parentheses. You can apply the Distributive Property or you can apply the Multiplication Property of Equality. This Concept will show you how to use the Distributive Property to solve multi-step equations.

#### Example A

*Solve for* *:*

**Solution:** Apply the Distributive Property:

Apply the Addition Property of Equality:

Simplify:

Apply the Multiplication Property of Equality:

The solution is .

Check: Does Yes, so the answer is correct.

#### Example B

Solve for when

**Solution:**

Checking the answer:

#### Example C

Solve for when

**Solution:**

Checking the answer:

### Vocabulary

**Distributive Property:** For any real numbers and :

**The Addition Property of Equality:** For all real numbers and :

If , then .

**The Multiplication Property of Equality:** For all real numbers , and :

*If* , *then*

### Guided Practice

*Solve for* when

**Solution:**

Step 1: Apply the Distributive Property.

Step 2: Combine like terms.

Step 3: Isolate the variable and its coefficient by using the Addition Property.

Step 4: Isolate the variable by applying the Multiplication Property.

Step 5: Check your answer.

Substitute into

Therefore,

### Practice

Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Multi-Step Equations (15:01)

Note that in the next video there IS an error. At one point the teacher says that -135/6 is in simplest form. There is a common factor of 3 in both numerator and denominator. -135/6 can be simplified by that factor of 3 to 45/2, or 22.5.

In 1 – 22, solve the equation.