# 7.4: Simplify Sums or Differences of Single Variable Expressions

**At Grade**Created by: CK-12

**Practice**Simplify Sums or Differences of Single Variable Expressions

Marc is heading to his local ice cream store. This particular store doesn't have a lot of flavor choices, but they have the BEST vanilla ice cream around. Marc has taken orders from several of his neighbors, too, and has written them all down so that he can keep track of who wants what.

The Johnsons - two vanilla ice cream cones

The Mumfords - three vanilla ice cream cones

Jill Stales - one vanilla ice cream cone

The Porters - three vanilla ice cream cones

How can Marc write this information as an algebraic expression and then simplify it?

In this concept, you will learn how to simplify single variable expressions.

### Simplifying Sums or Differences of Single Variable Expressions

If an expression has only numbers, you can calculate its numerical value. However, if an expression includes variables, it is helpful to simplify the expression.

Look at this example.

Simplify the expression

When adding expressions with variables, it is important to remember that only like terms can be combined. For example,

Here is another example.

Simplify

*not* like terms because only one term includes the variable

Here is another example.

Simplify

Since

The answer is

Here is an example using decimals.

Simplify

Since

The answer is

### Examples

#### Example 1

Earlier, you were given a problem about Marc and all of his ice cream orders.

Marc needs to write an expression to simplify his order: two vanillas, three vanillas, one vanilla, and three vanillas.

Let

Looking at this expression, you will see that the variables are all the same. Therefore, simply add the numerical part of each term.

The answer is

#### Example 2

Simplify the expression.

To simplify this expression, follow the order of operations and combine like terms in order from left to right. Here is what the expression looks like after the first two terms have been combined.

Next, perform the subtraction to get:

Finally, add the terms.

The answer is

**Simplify each sum or difference when possible.**

#### Example 3

These are like terms, so add the numerical parts together.

The answer is

#### Example 4

These are like terms, so subtract the numerical parts.

The answer is

#### Example 5

These are not like terms.

The terms are not alike so you cannot combine them. The expression is in the simplest form already.

The answer is

### Review

Simplify each sum or difference by combining like terms.

6a+7a 7x−2x 6y+12y 8a+12a 12y−7y 8a+15a 13b−9b 22x+19x 45y−12y 16a+18a+9a 14x−6x+2x 21a+14a−15a 33b+13b+8b 45x+67x−29x 92y+6y−54y

### Review (Answers)

To see the Review answers, open this PDF file and look for section 7.4.

### Resources

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Difference

The result of a subtraction operation is called a difference.Expression

An expression is a mathematical phrase containing variables, operations and/or numbers. Expressions do not include comparative operators such as equal signs or inequality symbols.Simplify

To simplify means to rewrite an expression to make it as "simple" as possible. You can simplify by removing parentheses, combining like terms, or reducing fractions.Sum

The sum is the result after two or more amounts have been added together.### Image Attributions

In this concept, you will learn how to simplify single variable expressions.

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