Writing Inequalities Using Word Problems

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

How do you represent a situation where a quantity is less than a certain value using an inequality?

Back

You can represent it using the symbol '<'. For example, if x is less than 5, it is written as x < 5.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is greater than 3.

Front

How do you write an inequality for a situation where a person has a limited budget?

Back

You can write it as an expression where the total cost is less than or equal to the budget. For example, if the budget is $100 and the cost is represented by C, then C ≤ 100.

Front

What is the first step in writing an inequality from a word problem?

Back

Identify the variables and the relationship between them based on the information given in the problem.

Front

In the problem 'Chris can rent a row boat for $40 plus $15 per hour. How many hours can he rent if he has less than $100?', how is the total cost represented?

Back

The total cost is represented as 40 + 15x, where x is the number of hours rented.

Front

What does the inequality 40 + 15x < 100 represent in the context of Chris renting a boat?

Back

It represents that the total cost of renting the boat for x hours must be less than $100.

Front

How do you solve the inequality 40 + 15x < 100 for x?

Back

Subtract 40 from both sides to get 15x < 60, then divide by 15 to find x < 4.

Front

In the cupcake problem, how do you express the total amount spent on cupcakes?

Back

The total amount spent is expressed as 8 + 5x, where x is the number of pink cupcakes bought.

Front

What does the inequality 8 + 5x ≤ 23 represent in the cupcake problem?

Back

It represents that the total amount spent on cupcakes must be less than or equal to $23.