What Is The Solution To This Inequality? − 13 X \textgreater − 39 -13x \ \textgreater \ -39 − 13 X \textgreater − 39 A. X \textless − 3 X \ \textless \ -3 X \textless − 3 B. X \textgreater − 3 X \ \textgreater \ -3 X \textgreater − 3 C. X \textless 3 X \ \textless \ 3 X \textless 3 D. X \textgreater 3 X \ \textgreater \ 3 X \textgreater 3

Introduction

In mathematics, inequalities are a fundamental concept that helps us compare the values of different variables. They are used to represent relationships between quantities, and solving them is an essential skill in algebra and other branches of mathematics. In this article, we will focus on solving a specific inequality, $-13x > -39$, and explore the different solution options.

Understanding the Inequality

The given inequality is $-13x > -39$. To solve this inequality, we need to isolate the variable $x$ on one side of the inequality sign. The first step is to divide both sides of the inequality by $-13$. However, when we divide or multiply an inequality by a negative number, we need to reverse the direction of the inequality sign.

Solving the Inequality

To solve the inequality, we will divide both sides by $-13$ and reverse the direction of the inequality sign.

$$-13x > -39$$

Dividing both sides by $-13$:

$$x < \frac{-39}{-13}$$

Simplifying the fraction:

$$x < 3$$

Analyzing the Solution Options

Now that we have solved the inequality, let's analyze the solution options:

A. $x < -3$ B. $x > -3$ C. $x < 3$ D. $x > 3$

From our solution, we can see that the correct answer is:

C. $x < 3$

This means that any value of $x$ that is less than $3$ will satisfy the inequality.

Conclusion

In conclusion, solving an inequality involves isolating the variable on one side of the inequality sign and reversing the direction of the inequality sign when dividing or multiplying by a negative number. By following these steps, we can solve the inequality $-13x > -39$ and determine that the correct solution is $x < 3$.

Frequently Asked Questions

Q: What is the first step in solving an inequality?

A: The first step in solving an inequality is to isolate the variable on one side of the inequality sign.

Q: What happens when we divide or multiply an inequality by a negative number?

A: When we divide or multiply an inequality by a negative number, we need to reverse the direction of the inequality sign.

Q: How do we simplify a fraction in an inequality?

A: To simplify a fraction in an inequality, we can divide both the numerator and the denominator by their greatest common divisor.

Tips and Tricks

Tip 1: Always check your work

When solving an inequality, it's essential to check your work by plugging in a value that satisfies the inequality to ensure that it's true.

Tip 2: Use inverse operations

To solve an inequality, you can use inverse operations to isolate the variable. For example, if the inequality is $x + 5 > 10$, you can subtract $5$ from both sides to get $x > 5$.

Tip 3: Be careful with negative numbers

When working with negative numbers, remember to reverse the direction of the inequality sign when dividing or multiplying by a negative number.

Real-World Applications

Inequalities have many real-world applications, such as:

• Modeling population growth or decline
• Representing financial transactions
• Describing physical phenomena, such as temperature or pressure

By understanding and solving inequalities, we can make informed decisions and solve real-world problems.

Final Thoughts

Solving inequalities is an essential skill in mathematics and has many real-world applications. By following the steps outlined in this article, you can solve inequalities and make informed decisions. Remember to always check your work, use inverse operations, and be careful with negative numbers. With practice and patience, you can become proficient in solving inequalities and tackle complex problems with confidence.

Introduction

In our previous article, we explored the solution to the inequality $-13x > -39$. In this article, we will delve deeper into the world of inequalities and provide a comprehensive Q&A guide to help you understand and solve inequalities with confidence.

Q&A Guide

Q: What is an inequality?

A: An inequality is a mathematical statement that compares two values or expressions using a symbol such as <, >, ≤, or ≥.

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. You can use inverse operations, such as addition, subtraction, multiplication, or division, to isolate the variable.

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 using a symbol such as <, >, ≤, or ≥.

Q: How do I handle negative numbers when solving an inequality?

A: When working with negative numbers, remember to reverse the direction of the inequality sign when dividing or multiplying by a negative number.

Q: Can I add or subtract the same value to both sides of an inequality?

A: Yes, you can add or subtract the same value to both sides of an inequality. This is known as adding or subtracting a constant.

Q: Can I multiply or divide both sides of an inequality by the same value?

A: Yes, you can multiply or divide both sides of an inequality by the same value. However, if you multiply or divide by a negative number, you need to reverse the direction of the inequality sign.

Q: How do I simplify a fraction in an inequality?

A: To simplify a fraction in an inequality, you can divide both the numerator and the denominator by their greatest common divisor.

Q: What is the order of operations when solving an inequality?

A: The order of operations when solving an inequality is the same as when solving an equation: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

Q: Can I use inverse operations to solve an inequality?

A: Yes, you can use inverse operations to solve an inequality. For example, if the inequality is $x + 5 > 10$, you can subtract $5$ from both sides to get $x > 5$.

Q: How do I check my work when solving an inequality?

A: To check your work, plug in a value that satisfies the inequality to ensure that it's true.

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

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

• Not reversing the direction of the inequality sign when dividing or multiplying by a negative number
• Not using inverse operations to isolate the variable
• Not checking your work

Real-World Applications

Inequalities have many real-world applications, such as:

• Modeling population growth or decline
• Representing financial transactions
• Describing physical phenomena, such as temperature or pressure

By understanding and solving inequalities, you can make informed decisions and solve real-world problems.

Final Thoughts

Solving inequalities is an essential skill in mathematics and has many real-world applications. By following the steps outlined in this article and practicing regularly, you can become proficient in solving inequalities and tackle complex problems with confidence.

Additional Resources

• Khan Academy: Inequalities
• Mathway: Inequality Solver
• Wolfram Alpha: Inequality Solver

Conclusion

In conclusion, solving inequalities is a crucial skill in mathematics that has many real-world applications. By understanding and solving inequalities, you can make informed decisions and solve complex problems with confidence. Remember to always check your work, use inverse operations, and be careful with negative numbers. With practice and patience, you can become proficient in solving inequalities and tackle complex problems with ease.