*Contributor: Erika Wargo. Lesson ID: 12893*

What does an alligator have to do with mathematics? It can help you remember when to use > and < and other math symbols. Learn how number sentences and variables are used to express inequalities!

categories

subject

Math

learning style

Visual

personality style

Otter

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

The new ride at the fair has height requirements.

The minimum height is 36 inches, and the maximum is 72 inches.

- If you are 62 inches tall, can you go on the ride?
- Which height would not be permitted to ride?

- Did you know that sometimes in math you don’t have to find the exact answer?

Most of the time, you try to solve an equation with one answer. An *equation* includes an equal sign (=) and represents two expressions that have the same value.

But sometimes, two expressions are greater than or less than each other and are represented using an inequality. *Inequalities* tell about expressions with different values.

Watch the video below to learn about inequalities.

Draw the special symbols representing each comparison in your math journal.

equal to | = |

not equal to | ≠ |

less than | < |

less than or equal to | ≤ |

greater than | > |

greater than or equal to | ≥ |

Then, write answers to these questions.

- Why are inequalities used?
- How can inequalities be used to represent real-world problems?

When using these symbols, be sure the wide part of the sign faces the greater value and the small part points toward the smaller number.

For example, to show that 15 is greater than 12, you would write 15 > 12.

One way to remember this is to think of the sign as an alligator’s mouth, and the alligator always wants to eat the larger side of the inequality!

An equation or inequality can be true or false, depending on the symbol used.

In some problems, you must substitute a value for the variable and solve it. In other problems, you might have to find a value resulting in a true or false number sentence.

A *number sentence* is a mathematical sentence — usually an equation or inequality — written with numbers and mathematical symbols.

**Examples:** Substitute 3 for x in each equation or inequality and evaluate. Determine if it results in a true number sentence or a false number sentence.

6 + x = 19

Substitute 3 for x, so 6 + 3 =9. 9 ≠19, so this number sentence is false.

4x = 12

Substitute 3 for x, so 4(3) = 12. This problem means multiplying, and 4 x 3 = 12, so this number sentence is true.

8 + x ≤ 12

Substitute 3 for x, so 8 + 3 = 11. 11 ≤ 12 means that 11 is less than or equal to 12, which is true. The inequality sign states that the expression on the left side must be less than or equal to the right.

Find a value for x to make this number sentence false: 39 - x ≥ 26.

First, find a number that would make the inequality true by being equal to 26. Since 39 - 13 = 26, if x = 13, the left side of the expression equals the right side.

The left side of the expression also needs to be greater than 26 to be true, so that would include numbers less than 13. If you want the expression to be false, choose numbers that make the equation's left side less than 26. In this example, x must be a number greater than or equal to 14 to be false.

**Example:** At the beginning of the lesson, you were presented with the following word problem.

The new ride at the fair has height requirements. The minimum height is 36 inches, and the maximum is 72 inches.

- If you are 62 inches tall, can you go on the ride?
- Which height would not be permitted to ride?

The minimum height is 36 inches, the smallest value allowed to ride. The maximum height is 72 inches, the greatest value allowed to ride.

If *h* stands for height, the inequalities would be h ≥ 36 and h ≤ 72. The rider must be equal to or greater than 36 inches but less than or equal to 72 inches.

If you are 62 inches, that is less than 72 inches, so you would be able to go on the ride. If you were 32 or 75 inches, you would not be able to go on the ride since your height is less than 36 inches or greater than 72 inches.

In your math journal, write a response to the following questions.

- What is the difference between these symbols: < and ≤?
- How do you determine if a number sentence is true or false?

Now, move on to the *Got It?* section to practice determining if equations and inequality statements are true or false.