Rosa Is Shopping For Books At Her School's Book Fair. She Found A Sale Shelf With Books All Priced At $\$ 12$ Or Less. Let $c$ Represent The Amount, In Dollars, That A Book On The Sale Shelf Might Cost. Which Inequality

Rosa's Book Fair Adventure: Solving Inequalities for a Great Deal

Rosa is shopping for books at her school's book fair, and she's excited to find a sale shelf with books priced at $12 or less. As she browses through the shelves, she wants to know which books she can afford within her budget. In this scenario, we'll represent the amount, in dollars, that a book on the sale shelf might cost as $c$. Our goal is to determine which inequality represents the possible values of $c$ that Rosa can afford.

To solve this problem, we need to understand the concept of inequalities and how they can be used to represent the possible values of a variable. In this case, we're looking for the values of $c$ that are less than or equal to $12$, since Rosa wants to buy books that cost $12 or less.

The inequality that represents the possible values of $c$ is:

$$c \leq 12$$

This inequality states that the value of $c$ is less than or equal to $12$. In other words, $c$ can take on any value that is less than or equal to $12$.

To solve the inequality, we need to isolate the variable $c$ on one side of the inequality sign. In this case, we can simply write:

$$c \leq 12$$

This is the solution to the inequality, and it represents the possible values of $c$ that Rosa can afford.

We can also graph the inequality on a number line to visualize the possible values of $c$. The number line will show all the values of $c$ that are less than or equal to $12$.

In real-world scenarios, inequalities are used to represent a wide range of situations, such as:

• Budgeting: Inequalities can be used to represent the possible values of a budget, such as the amount of money available for a project.
• Time: Inequalities can be used to represent the possible values of time, such as the amount of time available to complete a task.
• Distance: Inequalities can be used to represent the possible values of distance, such as the distance between two points.

In conclusion, the inequality $c \leq 12$ represents the possible values of $c$ that Rosa can afford to buy books at the sale shelf. By understanding and solving inequalities, we can make informed decisions in a wide range of situations.

Here are some additional examples of inequalities that represent possible values of a variable:

• $x \geq 5$: This inequality represents the possible values of $x$ that are greater than or equal to $5$.
• $y \leq 10$: This inequality represents the possible values of $y$ that are less than or equal to $10$.
• $z \geq 15$: This inequality represents the possible values of $z$ that are greater than or equal to $15$.

Here are some practice problems to help you understand and solve inequalities:

• Solve the inequality $x \geq 3$.
• Solve the inequality $y \leq 8$.
• Solve the inequality $z \geq 12$.

Here are the answers to the practice problems:

• $x \geq 3$: The solution to the inequality is $x \geq 3$.
• $y \leq 8$: The solution to the inequality is $y \leq 8$.
• $z \geq 12$: The solution to the inequality is $z \geq 12$.

In conclusion, inequalities are a powerful tool for representing possible values of a variable. By understanding and solving inequalities, we can make informed decisions in a wide range of situations. Whether it's budgeting, time, or distance, inequalities can help us navigate complex situations and make the most of our resources.
Rosa's Book Fair Adventure: Q&A on Inequalities

In our previous article, we explored the concept of inequalities and how they can be used to represent possible values of a variable. We also solved the inequality $c \leq 12$ to determine the possible values of $c$ that Rosa can afford to buy books at the sale shelf. In this article, we'll answer some frequently asked questions about inequalities to help you better understand this concept.

Q: What is an inequality?

A: An inequality is a statement that compares two values or expressions, indicating whether one is greater than, less than, or equal to the other.

Q: What are the different types of inequalities?

A: There are four main types of inequalities:

• Greater than ($>$): This inequality indicates that one value is greater than the other.
• Less than ($<$): This inequality indicates that one value is less than the other.
• Greater than or equal to ($\geq$): This inequality indicates that one value is greater than or equal to the other.
• Less than or equal to ($\leq$): This inequality indicates that one value is less than or equal to the other.

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable on one side of the inequality sign. This can involve adding, subtracting, multiplying, or dividing both sides of the inequality by the same value.

Q: What is the difference between an inequality and an equation?

A: An equation is a statement that says two values or expressions are equal, while an inequality is a statement that compares two values or expressions and indicates whether one is greater than, less than, or equal to the other.

Q: Can I use inequalities to solve real-world problems?

A: Yes, inequalities can be used to solve a wide range of real-world problems, such as budgeting, time, and distance.

Q: How do I graph an inequality on a number line?

A: To graph an inequality on a number line, you need to identify the values that satisfy the inequality and plot them on the number line.

Q: What are some common mistakes to avoid when solving inequalities?

A: Some common mistakes to avoid when solving inequalities include:

• Not isolating the variable: Make sure to isolate the variable on one side of the inequality sign.
• Not considering the direction of the inequality: Make sure to consider the direction of the inequality when solving the problem.
• Not checking the solution: Make sure to check the solution to ensure that it satisfies the inequality.

In conclusion, inequalities are a powerful tool for representing possible values of a variable. By understanding and solving inequalities, we can make informed decisions in a wide range of situations. Whether it's budgeting, time, or distance, inequalities can help us navigate complex situations and make the most of our resources.

Here are some additional resources to help you learn more about inequalities:

• Online tutorials: Websites such as Khan Academy and Mathway offer interactive tutorials and exercises to help you learn about inequalities.
• Textbooks: Many algebra textbooks include chapters on inequalities and how to solve them.
• Practice problems: Websites such as IXL and Math Open Reference offer practice problems and exercises to help you practice solving inequalities.

In conclusion, inequalities are a fundamental concept in mathematics that can be used to solve a wide range of real-world problems. By understanding and solving inequalities, we can make informed decisions and navigate complex situations with confidence.