# 3.16: Solve Inequalities Involving Combining Like Terms

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

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**Practice**Inequalities with Like Terms

### Let’s Think About It

**Credit**: Ogngen Odobasic

**Source**: https://www.flickr.com/photos/ognjenodobasic/4938876111/in/photolist-8wr2Np-4kmfFV-aQaGPv-5Ht8CM-7K12eo-bUrkwP-7C1wC5-aE3jtx-7JW7h4-bHfgH8-7wzTDN-aE8MrC-aQaHgB-7BWJbR-7JWdFR-7C1weL-aE8CSy-aE4mCZ-aE7xrf-aE7r6w-aE3svF-aE61od-aE4nj4-aE4pn2-aE5GvQ-aE4oGt-aE5QvL-aE5S7q-aE5MYA-aE5P43-aE22vV-aE1Y9V-aE5H4W-aE5R8y-aE5W4b-aE248R-aE5VFJ-aE22Kk-aE5J9o-aE5WHq-aE5JRw-aE5WXJ-9egMTU-aE24rB-5DNNFn-aE8tpA-aE2TMD-aE6RGA-aE33Wc-aE8utC

**License**: CC BY-NC 3.0

Your community center is selling boxes of cards. Your goal is to sell at least $500 worth of cards. Each box sells for $5 but you also need to pay the company $50 to ship all of the cards to your house to begin selling. Determine at least how many boxes of cards you must sell in order to meet your goal.

In this concept you will learn to solve inequalities involving combining like terms.

### Guidance

You can solve inequalities in many ways. Some inequalities can be solved in a single step. You could solve

However, two or more steps may be required to solve some inequalities. Inequalities that need more than one inverse operation to solve them can be called **multi-step inequalities**.

Let’s start by looking at combining like terms when you solve an inequality.

First, you can see that you have two terms that have the same variable. These are **like terms**. To solve an inequality with like terms, you will need to combine the like terms and then you can solve the inequality.

Here you divide both sides of the inequality by 7. Multiplication is the inverse operation of division.

The answer is

Let’s look at another example

Solve for

First, notice that there are two terms on the left side of the inequality, *added* to

The answer is

### Guided Practice

Here is one for you to try on your own.

Solve for

First, subtract

Next, isolate the term with the variable,

Then, since

The answer is

### Examples

#### Example 1

Solve for

First, isolate the term with the variable,

** **

4x+54x+5−54x<<<2121−516

Next, since

The answer is

#### Example 2

Solve for

First, isolate the term with the variable,

Next, since

The answer is

#### Example 3

Solve for

First, isolate the term with the variable,

Next, since

### Follow Up

**Credit**: Ogngen Odobasic

**Source**: https://www.flickr.com/photos/ognjenodobasic/4939466718/in/photolist-8wu4nh-aE3xnp-aE7AtE-aE7tU9-5FWUb1-7JZYcU-8wr2Np-4kmfFV-aQaGPv-5Ht8CM-7K12eo-bUrkwP-7C1wC5-aE3jtx-7JW7h4-bHfgH8-7wzTDN-aE8MrC-aQaHgB-7BWJbR-7JWdFR-7C1weL-aE8CSy-aE4mCZ-aE7xrf-aE7r6w-aE3svF-aE61od-aE4nj4-aE4pn2-aE5GvQ-aE4oGt-aE5QvL-aE5S7q-aE5MYA-aE5P43-aE22vV-aE1Y9V-aE5H4W-aE5R8y-aE5W4b-aE248R-aE5VFJ-aE22Kk-aE5J9o-aE5WHq-aE5JRw-aE5WXJ-9egMTU-aE24rB

**License**: CC BY-NC 3.0

Remember the boxes of cards being sold?

First, write an inequality using the given information. You want to raise at least $500 by selling boxes of cards worth $5 each. You also need to pay the supplier $50 for shipping. Let ‘

Next, isolate the term with the variable,

Next, since

The answer is

You need to sell at least 110 boxes of cards.

### Video Review

https://www.youtube.com/watch?v=XOAn5z8mkvI&feature=youtu.be

### Explore More

Solve each inequality.

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8.

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inequality

An inequality is a mathematical statement that relates expressions that are not necessarily equal by using an inequality symbol. The inequality symbols are , , , and .Inverse Operation

Inverse operations are operations that "undo" each other. Multiplication is the inverse operation of division. Addition is the inverse operation of subtraction.like terms

Terms are considered like terms if they are composed of the same variables with the same exponents on each variable.### Image Attributions

**[1]****^**Credit: Ogngen Odobasic; Source: https://www.flickr.com/photos/ognjenodobasic/4938876111/in/photolist-8wr2Np-4kmfFV-aQaGPv-5Ht8CM-7K12eo-bUrkwP-7C1wC5-aE3jtx-7JW7h4-bHfgH8-7wzTDN-aE8MrC-aQaHgB-7BWJbR-7JWdFR-7C1weL-aE8CSy-aE4mCZ-aE7xrf-aE7r6w-aE3svF-aE61od-aE4nj4-aE4pn2-aE5GvQ-aE4oGt-aE5QvL-aE5S7q-aE5MYA-aE5P43-aE22vV-aE1Y9V-aE5H4W-aE5R8y-aE5W4b-aE248R-aE5VFJ-aE22Kk-aE5J9o-aE5WHq-aE5JRw-aE5WXJ-9egMTU-aE24rB-5DNNFn-aE8tpA-aE2TMD-aE6RGA-aE33Wc-aE8utC; License: CC BY-NC 3.0**[2]****^**Credit: Ogngen Odobasic; Source: https://www.flickr.com/photos/ognjenodobasic/4939466718/in/photolist-8wu4nh-aE3xnp-aE7AtE-aE7tU9-5FWUb1-7JZYcU-8wr2Np-4kmfFV-aQaGPv-5Ht8CM-7K12eo-bUrkwP-7C1wC5-aE3jtx-7JW7h4-bHfgH8-7wzTDN-aE8MrC-aQaHgB-7BWJbR-7JWdFR-7C1weL-aE8CSy-aE4mCZ-aE7xrf-aE7r6w-aE3svF-aE61od-aE4nj4-aE4pn2-aE5GvQ-aE4oGt-aE5QvL-aE5S7q-aE5MYA-aE5P43-aE22vV-aE1Y9V-aE5H4W-aE5R8y-aE5W4b-aE248R-aE5VFJ-aE22Kk-aE5J9o-aE5WHq-aE5JRw-aE5WXJ-9egMTU-aE24rB; License: CC BY-NC 3.0

## Description

## Learning Objectives

In this concept, you will learn to solve inequalities involving combining like terms.

## Difficulty Level:

At Grade## Tags:

## Subjects:

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## Date Created:

Dec 19, 2012## Last Modified:

Aug 10, 2015## Vocabulary

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