Problem 15 - Prealgebra

Question

Write an inequality for each sentence. After a withdrawal, a savings account is now less than \(\$ 500\).

Step-by-Step Solution

Answer

The inequality is \( x < 500 \).

Step 1: Understanding the Problem

We need to express the situation given in words as an inequality. The sentence tells us that the amount in the savings account is less than \( \$500 \) after a withdrawal.

Step 2: Define the Variable

Let \( x \) represent the current balance in the savings account after the withdrawal.

Step 3: Write the Inequality

Since the account balance \( x \) is less than \( \$500 \), we can write the inequality as \( x < 500 \).

Key Concepts

Variables

Variables are fundamental concepts in mathematics, especially when dealing with expressions and equations. They are symbols, often represented by letters like \( x \), \( y \), or \( z \), used to represent unknown or variable quantities in equations and inequalities. In this exercise, we chose \( x \) as a variable to stand for the current balance in the savings account after a withdrawal. By introducing a variable, we simplify the task of solving problems as we can easily manipulate the equation or inequality to isolate the variable and find its value. Variables serve as placeholders that can change depending on the values we assign them, making them crucial for expressing mathematical relationships and solving problems.

Inequality Expressions

Inequality expressions are statements that use inequality symbols such as \( < \), \( > \), \( \leq \), and \( \geq \) to compare two values or expressions. They are essential in describing a range of possible solutions rather than a single value. For instance, in our exercise, the inequality \( x < 500 \) indicates that the account balance must be any value less than 500 dollars after a withdrawal.

• \( < \) means "less than,"
• \( > \) signifies "greater than,"
• \( \leq \) indicates "less than or equal to,"
• \( \geq \) signifies "greater than or equal to."

These symbols help in setting up conditions and constraints in real-world problems and are widely used in financial contexts, physics, engineering, and many other fields. Understanding how to read and write inequality expressions can significantly enhance one's analytical skills.

Savings Account

A savings account is a type of bank account where individuals can store money securely and earn interest over time. It is primarily used for setting aside funds for future use, such as emergencies, purchases, or as part of a budgeting strategy. Savings accounts are important because they not only keep money safe but also offer an opportunity to grow wealth through earned interest.

Banks usually impose rules on savings accounts, such as minimum balance requirements or limits on withdrawals per month. In our exercise, understanding that the savings account balance has to remain below \(\$500\) is an example of using inequalities to manage financial thresholds effectively. Knowing how to represent financial conditions via mathematical expressions is a key component of financial literacy.

Financial Literacy

Financial literacy refers to the knowledge and understanding of various financial concepts and the ability to apply them in everyday life. It includes the ability to manage personal finances effectively, which involves budgeting, saving, investing, and understanding credit and debt management.

Financial literacy equips individuals with the skills needed to make informed financial decisions and is a critical skill in today's complex financial world. In this exercise, by learning to write an inequality to represent a financial situation, you are enhancing your financial literacy.

• Setting and reaching savings goals
• Understanding the impact of interest rates on loans or savings
• Evaluating financial products and their terms

These are just a few examples of how financial literacy can be applied. Gaining proficiency in interpreting and writing financial inequalities can aid in better budget management and cash flow analysis, ultimately leading to greater financial security and success.