Equations and Inequalities: Real-World Situations

Contributor: Erika Wargo. Lesson ID: 12894

Sometimes, students wonder what good math lessons will do for them in real life. When will they use what they study? Learn why these symbols, <, =, > -- and more -- are important in your real world!


Middle School

learning style
personality style
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!


Beyoncé’s engagement ring from Jay Z is valued at more than $5 million. What are two possible values for the price of the ring? How can you use a number sentence to represent this amount?

Inequalities and equations are used all the time in the world around you.

Before you continue on, if you missed or would like to review the previous lesson in this Equations and Inequalities series, find it under Related Lessons in the right-hand sidebar.

The situations may not seem like math to you because you are so familiar with them. If you have a cell phone, you might have a certain number of text messages or phone calls that you can use each month. Roads have speed limits, certain movies have age restrictions, and the time it takes you to walk to the park are all examples of inequalities. Inequalities do not represent an exact amount, but instead represent a limit of what is allowed or what is possible. Equations represent values that are equal.

To begin, watch a MooMoo Math and Science video clip to learn about inequality word problems. As you watch Solving Inequalities-Word Problems-6th Grade Math, write down phrases that represent the given comparison symbol in your math journal (clip ends at 0:57):

> <



After the video, review the table in this interactive to be sure you have all of the phrases from the video. Click on each symbol to read the phrases that represent it in an inequality:

Next, watch Word Problem Inequalities by Shmoop to learn how to create an inequality from a word problem. Respond to the following questions in your math journal:

  1. The open part of a comparison symbol faces which value?
  2. What is the difference between the “greater than” symbol and the “greater than or equal to” symbol?
  3. What do you think is the difference between an inequality and an equation?

Discuss the questions above with a parent or teacher after watching the video clip (ends at 2:21):


As you saw in the videos above, inequalities include special signs to indicate which side is bigger or smaller, or to show that the two sides are not equal. Equations use an equal sign (=) to show that both sides of the equation are equal to each other. The open part of the comparison symbol always faces the greater value.

Number sentences are used to represent equations and inequalities. A number sentence is a mathematical sentence that is written using numerals and mathematical symbols, such as comparison symbols, an equal sign, and operation symbols. Operation symbols indicate which operation you should use to solve the problem: addition, subtraction, multiplication, or division. If an amount is unknown, a variable is used to represent the amount. A variable is any letter. You can choose a letter that relates to the word problem or choose any letter you want.

If a symbol contains “equal to”, such as “greater than or equal to” or “less than or equal to”, the expressions on both sides of the symbol have to equal each other. If the “less than” or “greater than” symbol is used, the expressions cannot be equal to each other.

equal to =
not equal to
less than <
less than or equal to
greater than >
greater than or equal to


Example Translate the expression into a number sentence:

  1. Tanner spent more than $24.
    • The phrase “more than” $24 means that he did not spend exactly $24, so “equal to” cannot be used. The number sentence would be: t > $24.
    • Remember, the variable can be any letter and it does not have to be a “t.” As long as the symbol and numbers used are correct, you can use any letter for the variable.
  2. Frankie walked 15 miles to school.
    • The expression does not indicate that Frankie walked more or less than 15 miles, so you can assume he walked exactly 15 miles. The number sentence to represent this would be: w = 15.
  3. Children age 10 and under are admitted to the concert for free.
    • The phrase “10 and under” indicates that the child can be 10 or less than 10. The age must be “less than or equal to 10,” which is written: a ≤ 10.

Example At the beginning of the lesson, you were presented with this word problem:

Beyoncé’s engagement ring from Jay Z is valued at more than $5 million. What are two possible values for the price of the ring? How can you use a number sentence to represent this amount?

Since the value of the ring is “more than” $5 million, the possible values have to be greater than $5 million. There are many possibilities but two examples could be $6 million or $5.5 million.

The key phrase is “more than,” which means that you will use the "greater than" symbol. A number sentence to represent this situation would be: r > $5 million.

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

  • How can you determine if you use “equal to” in your inequality comparison?
  • Can an equation, with an equal sign, have more than one solution? Explain.

Now, you will move on to the Got It? section to complete interactive practice in writing number sentences for real-world statements.

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