### Key Concepts

- Understand inequalities.
- Write inequalities.

**Introduction**

## Meaning of Inequality:

Inequality means a mathematical expression in which the sides are not equal to each other. Basically, an inequality compares any two values and shows that one value is less than, greater than, or equal to the value on the other side of the equation.

You can write an inequality to show a relationship in a real-world situation. For example, you could write an inequality to show that there were more than 50 people at a picnic. Or you could write an inequality to show that you can spend up to $15.00 at a store.

An inequality is a mathematical sentence that contains an inequality symbol.

The following table shows the inequality symbols.

**4.6.1 Understand inequalities**

**Example 1:**

How can you write an inequality to show that there were more than 60 people at a picnic?

Here are some numbers of people that might have been at the picnic:

62, 67, 70, 82

**Solution:**

There were more than 60 people at the picnic, so every possible number will be greater than 60.

Use the variable *p* to represent the number of people at the picnic. Use the greater than symbol (>) to write the inequality.

**Example 2:**

Jack won a blue ribbon for growing the heaviest pumpkin in a contest. It weighed 213 pounds. What could be the weights of other pumpkins in the contest? How could you show the weights of the other pumpkins using a mathematical statement? Explain.

**Solution:**

**Step 1:** You can show some of the weights on a number line.

**Step 2:** Let *x* represent the weights of other pumpkins. Use the less than symbol (<) to write the inequality.

**4.6.2 Write inequalities**

**Example 3:**

The stadium had seating for 30,000 fans, and it was not full. Write an inequality to show the number of fans at the game. Write an inequality to represent this situation.

**Solution:**

**Example 4:**

The museum gave a discount to seniors over the age of 65. Write an inequality to represent the age of the seniors who receive a discount. Write an inequality to represent this situation.

**Solution:**

**Example 5:**

There can be up to 25 dogs, (d), at a dog park. Write an inequality to represent this situation.

**Solution:**

**Example 6:**

Campfires must be at least 30 feet from the nearest tent. Write an inequality to show distance from a campfire to the nearest tent. Write an inequality to represent this situation.

**Solution:**

**Example 7:**

Students may not work in groups of 4. Write an inequality to represent the number of students that may be in a group. Write an inequality to represent this situation.

**Solution:**

### Concept Map

## Exercise:

1. How do you know when to use the less than symbol and when to use the less than or equal to symbol when writing an inequality for a situation?

2. Write a real-world situation that can be represented by x < 5.

3. A bucket, b, holds up to 3 gallons. Write an inequality to represent this situation.

4. The first bookcase, A, in a library can hold 1 more book than the second bookcase. The second bookcase holds 1,493 books. Write an inequality to represent the number of books the first bookcase can hold.

5. A certain airplane must carry no more than 158 passengers during a flight. Write an inequality to represent the number of passengers, p, that would NOT be allowed during this flight

6. Chloe’s age, a, is under 5. Write an inequality to represent this situation.

7. The temperature, 4 is over 820. Write an inequality to represent this situation.

8. The width, w, is at least 10 feet Write an inequality to represent this situation.

9. Terry had less than 40 minutes to finish his work Then he got a phone call that lasted 15 minutes. Write an inequality to show how much time he has left to work

10. Sara practices the piano as much as 3 hours a day from Monday through Thursday, and she practices up to 3 hours on Saturday. Write an inequality to show the number of hours that she practices in one week

### What have we learned:

■ Understand inequalities and the symbols used to write inequalities.

■ Write inequalities for the given situation.

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