Equations and Inequalities: Real-World Situations (2024)

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; however, the situations may not seem like math because you are familiar with them.

If you have a cell phone, you might have a certain number of text messages or phone calls 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 possible. Equations represent values that are equal.

Learn about inequality word problems. Create a chart similar to the one below in your math journal.

• Did you complete your chart with the phrases from the video?

Click on each symbol below to read the phrases representing it in an inequality and adjust your chart if necessary.

Next, watch the following video on creating an inequality from a word problem.

Respond to the following questions in your math journal.

• The open part of a comparison symbol faces which value?
• What is the difference between the greater than symbol and the greater than or equal to symbol?
• What is the difference between an inequality and an equation?

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 are equal. 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 written using numerals and mathematical symbols, such as comparison symbols, equal signs, 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 represents the amount. A variable is any letter. You can choose a letter related to the word problem or 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.

Examples: Translate each expression into a number sentence.

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 does not have to be a t. As long as the symbol and numbers are correct, you can use any letter for the variable.

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.

Children aged 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 the following word problem.

Beyoncé’s engagement ring from Jay Z is valued at more than $5 million.

• What are two possible values for the ring's price?
• How can you use a number sentence to represent this amount?

Since the ring's value is “more than $5 million," the possible values must 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,” requiring the greater than symbol. A number sentence to represent this situation would be r > $5 million.

Write responses to the following questions in your math journal.

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