Which Statement Is True?A. $-1.2 \ \textless \ 6.9$B. $-6.9 \ \textgreater \ -1.2$C. $1.2 \ \textless \ -6.9$D. $6.9 \ \textless \ 1.2$

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Introduction

In mathematics, inequalities are a fundamental concept that helps us compare the magnitude of two or more numbers. They are used to express the relationship between two or more quantities, and are essential in various mathematical operations, including algebra, geometry, and calculus. In this article, we will explore the concept of inequalities, and help you understand which statement is true among the given options.

What are Inequalities?

Inequalities are mathematical statements that compare two or more numbers, and indicate whether one is greater than, less than, or equal to the other. They are denoted by the use of symbols such as <, >, ≤, and ≥. For example, the statement "x > 5" means that x is greater than 5, while the statement "x < 5" means that x is less than 5.

Types of Inequalities

There are several types of inequalities, including:

  • Linear inequalities: These are inequalities that involve a linear expression, such as x + 2 > 3.
  • Quadratic inequalities: These are inequalities that involve a quadratic expression, such as x^2 + 2x + 1 > 0.
  • Absolute value inequalities: These are inequalities that involve the absolute value of a number, such as |x| > 2.

Understanding the Given Options

Now that we have a basic understanding of inequalities, let's examine the given options:

A. −1.2 \textless 6.9-1.2 \ \textless \ 6.9 B. −6.9 \textgreater −1.2-6.9 \ \textgreater \ -1.2 C. 1.2 \textless −6.91.2 \ \textless \ -6.9 D. 6.9 \textless 1.26.9 \ \textless \ 1.2

Analyzing Option A

Option A states that −1.2 \textless 6.9-1.2 \ \textless \ 6.9. To determine whether this statement is true, we need to compare the two numbers. Since -1.2 is less than 6.9, this statement is indeed true.

Analyzing Option B

Option B states that −6.9 \textgreater −1.2-6.9 \ \textgreater \ -1.2. To determine whether this statement is true, we need to compare the two numbers. Since -6.9 is indeed greater than -1.2, this statement is also true.

Analyzing Option C

Option C states that 1.2 \textless −6.91.2 \ \textless \ -6.9. To determine whether this statement is true, we need to compare the two numbers. Since 1.2 is not less than -6.9, this statement is false.

Analyzing Option D

Option D states that 6.9 \textless 1.26.9 \ \textless \ 1.2. To determine whether this statement is true, we need to compare the two numbers. Since 6.9 is not less than 1.2, this statement is also false.

Conclusion

In conclusion, the correct answer is option A, −1.2 \textless 6.9-1.2 \ \textless \ 6.9. This statement is true because -1.2 is indeed less than 6.9. We hope this article has helped you understand the concept of inequalities and how to analyze them.

Final Thoughts

Inequalities are a fundamental concept in mathematics, and are used to express the relationship between two or more quantities. By understanding the different types of inequalities and how to analyze them, you can solve a wide range of mathematical problems. We hope this article has been helpful in your understanding of inequalities, and we wish you the best in your mathematical endeavors.

Additional Resources

If you are looking for additional resources to help you understand inequalities, we recommend the following:

  • Math textbooks: There are many excellent math textbooks that cover the concept of inequalities in detail.
  • Online resources: There are many online resources, including websites and video tutorials, that can help you understand inequalities.
  • Practice problems: Practice problems are an excellent way to reinforce your understanding of inequalities and to develop your problem-solving skills.

References

  • "Algebra and Trigonometry" by Michael Sullivan: This textbook provides a comprehensive introduction to algebra and trigonometry, including the concept of inequalities.
  • "Mathematics for Dummies" by Mark Ryan: This book provides a comprehensive introduction to mathematics, including the concept of inequalities.
  • "Khan Academy": This website provides a wide range of video tutorials and practice problems on mathematics, including inequalities.

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Introduction

In our previous article, we explored the concept of inequalities and how to analyze them. In this article, we will answer some of the most frequently asked questions about inequalities.

Q: What is the difference between < and >?

A: The symbols < and > are used to indicate that one number is less than or greater than another number, respectively. For example, x < 5 means that x is less than 5, while x > 5 means that x is greater than 5.

Q: What is the difference between ≤ and ≥?

A: The symbols ≤ and ≥ are used to indicate that one number is less than or equal to or greater than or equal to another number, respectively. For example, x ≤ 5 means that x is less than or equal to 5, while x ≥ 5 means that x is greater than or equal to 5.

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 be done by adding or subtracting the same value to both sides of the inequality, or by multiplying or dividing both sides of the inequality by the same non-zero value.

Q: What is the order of operations for inequalities?

A: The order of operations for inequalities is the same as for equations: parentheses, exponents, multiplication and division, and addition and subtraction.

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. For example, if you have the inequality x < 5, you can add 2 to both sides to get x + 2 < 7.

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

A: Yes, you can multiply or divide both sides of an inequality by the same non-zero value. For example, if you have the inequality x < 5, you can multiply both sides by 2 to get 2x < 10.

Q: What is the difference between a linear inequality and a quadratic inequality?

A: A linear inequality is an inequality that involves a linear expression, such as x + 2 < 3. A quadratic inequality is an inequality that involves a quadratic expression, such as x^2 + 2x + 1 > 0.

Q: How do I solve a quadratic inequality?

A: To solve a quadratic inequality, you need to factor the quadratic expression and then use the sign of the expression to determine the solution set.

Q: What is the difference between an absolute value inequality and a linear inequality?

A: An absolute value inequality is an inequality that involves the absolute value of a number, such as |x| > 2. A linear inequality is an inequality that involves a linear expression, such as x + 2 < 3.

Q: How do I solve an absolute value inequality?

A: To solve an absolute value inequality, you need to isolate the absolute value expression and then use the sign of the expression to determine the solution set.

Conclusion

In conclusion, inequalities are a fundamental concept in mathematics, and are used to express the relationship between two or more quantities. By understanding the different types of inequalities and how to analyze them, you can solve a wide range of mathematical problems. We hope this article has been helpful in your understanding of inequalities, and we wish you the best in your mathematical endeavors.

Additional Resources

If you are looking for additional resources to help you understand inequalities, we recommend the following:

  • Math textbooks: There are many excellent math textbooks that cover the concept of inequalities in detail.
  • Online resources: There are many online resources, including websites and video tutorials, that can help you understand inequalities.
  • Practice problems: Practice problems are an excellent way to reinforce your understanding of inequalities and to develop your problem-solving skills.

References

  • "Algebra and Trigonometry" by Michael Sullivan: This textbook provides a comprehensive introduction to algebra and trigonometry, including the concept of inequalities.
  • "Mathematics for Dummies" by Mark Ryan: This book provides a comprehensive introduction to mathematics, including the concept of inequalities.
  • "Khan Academy": This website provides a wide range of video tutorials and practice problems on mathematics, including inequalities.