Solve For A A A In The Inequality: − 51 + 9 A \textgreater − 33 -51 + 9a \ \textgreater \ -33 − 51 + 9 A \textgreater − 33 Choose The Correct Inequality Symbol:- $\ \textless \ $- ≥ \geq ≥ - ≤ \leq ≤ - = = =

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Introduction

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In mathematics, inequalities are a fundamental concept that plays a crucial role in solving various problems. An inequality is a statement that two expressions are not equal, but one is greater than or less than the other. In this article, we will focus on solving inequalities, specifically the inequality $-51 + 9a > -33$. We will break down the steps to solve this inequality and choose the correct inequality symbol.

Understanding the Inequality

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The given inequality is $-51 + 9a > -33$. To solve this inequality, we need to isolate the variable $a$ on one side of the inequality. The first step is to add $51$ to both sides of the inequality to get rid of the negative term.

-51 + 9a > -33
-51 + 51 + 9a > -33 + 51
0 + 9a > 18
9a > 18

Isolating the Variable

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Now that we have isolated the variable $a$ on one side of the inequality, we need to get rid of the coefficient $9$ that is multiplied by $a$. To do this, we divide both sides of the inequality by $9$.

9a > 18
\frac{9a}{9} > \frac{18}{9}
a > 2

Choosing the Correct Inequality Symbol

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Now that we have solved the inequality, we need to choose the correct inequality symbol. The inequality symbol that represents the relationship between the two expressions is the one that is used to indicate that the expression on the left-hand side is greater than the expression on the right-hand side.

In this case, the correct inequality symbol is $\textgreater$.

Conclusion

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Solving inequalities requires a step-by-step approach. We need to isolate the variable on one side of the inequality and get rid of any coefficients that are multiplied by the variable. Once we have solved the inequality, we need to choose the correct inequality symbol to represent the relationship between the two expressions. In this article, we solved the inequality $-51 + 9a > -33$ and chose the correct inequality symbol.

Frequently Asked Questions

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Q: What is an inequality?

A: An inequality is a statement that two expressions are not equal, but one is greater than or less than 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 and get rid of any coefficients that are multiplied by the variable.

Q: What is the correct inequality symbol for the inequality $a > 2$?

A: The correct inequality symbol for the inequality $a > 2$ is $\textgreater$.

Tips and Tricks

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Tip 1: Always isolate the variable on one side of the inequality.

Isolating the variable on one side of the inequality makes it easier to solve the inequality.

Tip 2: Get rid of any coefficients that are multiplied by the variable.

Getting rid of any coefficients that are multiplied by the variable makes it easier to solve the inequality.

Tip 3: Choose the correct inequality symbol.

Choosing the correct inequality symbol is important to represent the relationship between the two expressions.

Real-World Applications

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Solving inequalities has many real-world applications. For example, in finance, inequalities are used to calculate interest rates and investment returns. In engineering, inequalities are used to design and optimize systems. In medicine, inequalities are used to model and analyze the spread of diseases.

Conclusion

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Solving inequalities is an important concept in mathematics that has many real-world applications. By following the steps outlined in this article, you can solve inequalities and choose the correct inequality symbol. Remember to always isolate the variable on one side of the inequality and get rid of any coefficients that are multiplied by the variable. With practice and patience, you can become proficient in solving inequalities and apply them to real-world problems.

References

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• [1] "Inequalities" by Math Open Reference. [Online]. Available: https://www.mathopenref.com/inequality.html
• [2] "Solving Inequalities" by Khan Academy. [Online]. Available: https://www.khanacademy.org/math/algebra/x2-ineq/x2-ineq-solve
• [3] "Inequalities in Finance" by Investopedia. [Online]. Available: https://www.investopedia.com/terms/i/inequality.asp

Further Reading

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• "Algebra" by Michael Artin
• "Calculus" by Michael Spivak
• "Linear Algebra" by Jim Hefferon

Related Topics

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• Solving Equations
• Graphing Inequalities
• Systems of Inequalities

Glossary

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• Inequality: A statement that two expressions are not equal, but one is greater than or less than the other.
• Variable: A symbol that represents a value that can change.
• Coefficient: A number that is multiplied by a variable.
• Inequality Symbol: A symbol that represents the relationship between two expressions, such as $\textgreater$ or $\textless$.

License

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This article is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

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Introduction

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In our previous article, we discussed how to solve inequalities and choose the correct inequality symbol. In this article, we will provide a Q&A guide to help you understand and apply the concepts of solving inequalities.

Q&A

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Q: What is an inequality?

A: An inequality is a statement that two expressions are not equal, but one is greater than or less than 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 and get rid of any coefficients that are multiplied by the variable.

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

A: A linear inequality is an inequality that can be written in the form $ax + b > c$ or $ax + b < c$, where $a$, $b$, and $c$ are constants. A quadratic inequality is an inequality that can be written in the form $ax^2 + bx + c > 0$ or $ax^2 + bx + c < 0$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you need to isolate the variable on one side of the inequality and get rid of any coefficients that are multiplied by the variable. For example, to solve the inequality $2x + 3 > 5$, you would first subtract 3 from both sides to get $2x > 2$, and then divide both sides by 2 to get $x > 1$.

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. For example, to solve the inequality $x^2 + 4x + 4 > 0$, you would first factor the expression to get $(x + 2)^2 > 0$, and then use the sign of the expression to determine that the solution set is $x > -2$.

Q: What is the difference between a strict inequality and a non-strict inequality?

A: A strict inequality is an inequality that is written with a strict inequality symbol, such as $>$ or $<$. A non-strict inequality is an inequality that is written with a non-strict inequality symbol, such as $\geq$ or $\leq$.

Q: How do I choose the correct inequality symbol?

A: To choose the correct inequality symbol, you need to determine the relationship between the two expressions. If the expression on the left-hand side is greater than the expression on the right-hand side, you would use the $>$ symbol. If the expression on the left-hand side is less than the expression on the right-hand side, you would use the $<$ symbol.

Q: Can I use the same steps to solve a system of inequalities as I would to solve a system of equations?

A: No, you cannot use the same steps to solve a system of inequalities as you would to solve a system of equations. When solving a system of inequalities, you need to find the solution set that satisfies all of the inequalities in the system.

Tips and Tricks

---

Tip 1: Always isolate the variable on one side of the inequality.

Isolating the variable on one side of the inequality makes it easier to solve the inequality.

Tip 2: Get rid of any coefficients that are multiplied by the variable.

Getting rid of any coefficients that are multiplied by the variable makes it easier to solve the inequality.

Tip 3: Choose the correct inequality symbol.

Choosing the correct inequality symbol is important to represent the relationship between the two expressions.

Real-World Applications

---

Solving inequalities has many real-world applications. For example, in finance, inequalities are used to calculate interest rates and investment returns. In engineering, inequalities are used to design and optimize systems. In medicine, inequalities are used to model and analyze the spread of diseases.

Conclusion

---

Solving inequalities is an important concept in mathematics that has many real-world applications. By following the steps outlined in this article, you can solve inequalities and choose the correct inequality symbol. Remember to always isolate the variable on one side of the inequality and get rid of any coefficients that are multiplied by the variable. With practice and patience, you can become proficient in solving inequalities and apply them to real-world problems.

References

---

• [1] "Inequalities" by Math Open Reference. [Online]. Available: https://www.mathopenref.com/inequality.html
• [2] "Solving Inequalities" by Khan Academy. [Online]. Available: https://www.khanacademy.org/math/algebra/x2-ineq/x2-ineq-solve
• [3] "Inequalities in Finance" by Investopedia. [Online]. Available: https://www.investopedia.com/terms/i/inequality.asp

Further Reading

---

• "Algebra" by Michael Artin
• "Calculus" by Michael Spivak
• "Linear Algebra" by Jim Hefferon

Related Topics

---

• Solving Equations
• Graphing Inequalities
• Systems of Inequalities

Glossary

---

• Inequality: A statement that two expressions are not equal, but one is greater than or less than the other.
• Variable: A symbol that represents a value that can change.
• Coefficient: A number that is multiplied by a variable.
• Inequality Symbol: A symbol that represents the relationship between two expressions, such as $\textgreater$ or $\textless$.

License

---

This article is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.